diff --git a/Makefile b/Makefile
index 83dec9686..6d5f6f33a 100644
--- a/Makefile
+++ b/Makefile
@@ -7,6 +7,7 @@ DEV_CONTAINER_CACHE_VOLUME:=concretefhe-internal-cache
 SRC_DIR:=concrete
 NOTEBOOKS_DIR:=docs/user/advanced_examples
 
+.PHONY: setup_env # Set up the environment
 setup_env:
 	poetry run python -m pip install -U pip wheel
 	poetry run python -m pip install -U --force-reinstall setuptools
@@ -21,81 +22,83 @@ setup_env:
 			poetry run python -m pip install /pkg/*.whl;	\
 		fi;													\
 	fi
-.PHONY: setup_env
 
+.PHONY: sync_env # Synchronise the environment
 sync_env:
 	poetry install --remove-untracked
 	$(MAKE) setup_env
-.PHONY: sync_env
 
+.PHONY: python_format # Apply python formatting
 python_format:
 	poetry run env bash ./script/source_format/format_python.sh \
 	--dir $(SRC_DIR) --dir tests --dir benchmarks --dir script
-.PHONY: python_format
 
+.PHONY: check_python_format # Check python format
 check_python_format:
 	poetry run env bash ./script/source_format/format_python.sh \
 	--dir $(SRC_DIR) --dir tests --dir benchmarks --dir script --check
-.PHONY: check_python_format
 
+.PHONY: check_finalize_nb # Sanitize notebooks
 check_finalize_nb:
 	poetry run python ./script/nbmake_utils/notebook_finalize.py $(NOTEBOOKS_DIR) --check
-.PHONY: check_finalize_nb
 
+.PHONY: check_benchmarks # Run benchmark checks (to validate they work fine)
 check_benchmarks:
 	poetry run python script/progress_tracker_utils/extract_machine_info.py
 	poetry run python script/progress_tracker_utils/measure.py benchmarks --check
-.PHONY: check_benchmarks
 
+.PHONY: pylint # Run pylint
 pylint:
 	$(MAKE) --keep-going pylint_src pylint_tests pylint_benchmarks pylint_script
-.PHONY: pylint
 
+.PHONY: pylint_src # Run pylint on sources
 pylint_src:
 	poetry run pylint --rcfile=pylintrc $(SRC_DIR)
-.PHONY: pylint_src
 
+.PHONY: pylint_tests # Run pylint on tests
 pylint_tests:
 	@# Disable duplicate code detection (R0801) in tests
 	@# Disable unnecessary lambda (W0108) for tests
 	find ./tests/ -type f -name "*.py" | xargs poetry run pylint --disable=R0801,W0108 --rcfile=pylintrc
-.PHONY: pylint_tests
 
+.PHONY: pylint_benchmarks # Run pylint on benchmarks
 pylint_benchmarks:
 	@# Disable duplicate code detection, docstring requirement, too many locals/statements
 	find ./benchmarks/ -type f -name "*.py" | xargs poetry run pylint \
 	--disable=R0801,R0914,R0915,C0103,C0114,C0115,C0116 --rcfile=pylintrc
-.PHONY: pylint_benchmarks
 
+.PHONY: pylint_script # Run pylint on scripts
 pylint_script:
 	@# disable linting python files under `progress_tracker_utils/test_scripts` folder
 	@# because they are intentionally ill-formed so that progress tracker can be tested
 	find ./script/ -type f -name "*.py" -not -path "./script/progress_tracker_utils/test_scripts/*" | xargs poetry run pylint --rcfile=pylintrc
-.PHONY: pylint_script
 
+.PHONY: flake8 # Run flake8
 flake8:
 	poetry run flake8 --max-line-length 100 --per-file-ignores="__init__.py:F401" \
 	$(SRC_DIR)/ tests/ benchmarks/ script/
-.PHONY: flake8
 
+.PHONY: python_linting # Run python linters
 python_linting: pylint flake8
-.PHONY: python_linting
 
+.PHONY: conformance # Run command to fix some conformance issues automatically
 conformance: finalize_nb python_format supported_functions licences
-.PHONY: conformance
 
+.PHONY: pcc # Run pre-commit checks
 pcc:
 	@$(MAKE) --keep-going --jobs $(./script/make_utils/ncpus.sh) --output-sync=recurse \
 	--no-print-directory pcc_internal
-.PHONY: pcc
 
 PCC_DEPS := check_python_format check_finalize_nb python_linting mypy_ci pydocstyle shell_lint
 PCC_DEPS += check_version_coherence check_supported_functions check_benchmarks check_licences
-pcc_internal: $(PCC_DEPS)
+
+# Not commented on purpose for make help, since internal
 .PHONY: pcc_internal
+pcc_internal: $(PCC_DEPS)
 
 # One can reproduce pytest thanks to the --randomly-seed which is given by
 # pytest-randomly
+.PHONY: pytest # Run pytest
 pytest:
 	poetry run pytest -svv \
 	--global-coverage-infos-json=global-coverage-infos.json \
@@ -103,60 +106,60 @@ pytest:
 	--cov=$(SRC_DIR) --cov-fail-under=100 \
 	--randomly-dont-reorganize \
 	--cov-report=term-missing:skip-covered tests/
-.PHONY: pytest
 
+.PHONY: pytest_progress_tracker # Run pytest for progress tracker
 pytest_progress_tracker:
 	poetry run python script/progress_tracker_utils/extract_machine_info.py
 	poetry run pytest -svv script/progress_tracker_utils/test_progress_tracker.py
-.PHONY: pytest_progress_tracker
 
 # Not a huge fan of ignoring missing imports, but some packages do not have typing stubs
+.PHONY: mypy # Run mypy
 mypy:
 	poetry run mypy -p $(SRC_DIR) --ignore-missing-imports
-.PHONY: mypy
 
 # Friendly target to run mypy without ignoring missing stubs and still have errors messages
 # Allows to see which stubs we are missing
+.PHONY: mypy_ns # Run mypy (without ignoring missing stubs)
 mypy_ns:
 	poetry run mypy -p $(SRC_DIR)
-.PHONY: mypy_ns
 
+.PHONY: mypy_test # Run mypy on test files
 mypy_test:
 	find ./tests/ -name "*.py" | xargs poetry run mypy --ignore-missing-imports
-.PHONY: mypy_test
 
+.PHONY: mypy_benchmark # Run mypy on benchmark files
 mypy_benchmark:
 	find ./benchmarks/ -name "*.py" | xargs poetry run mypy --ignore-missing-imports
-.PHONY: mypy_benchmark
 
+.PHONY: mypy_script # Run mypy on scripts
 mypy_script:
 	find ./script/ -name "*.py" | xargs poetry run mypy --ignore-missing-imports
-.PHONY: mypy_script
 
 # The plus indicates that make will be called by the command and allows to share the context with
 # the parent make execution. We serialize calls to these targets as they may overwrite each others
 # cache which can cause issues.
+.PHONY: mypy_ci # Run all mypy checks for CI
 mypy_ci:
 	$(MAKE) --keep-going mypy mypy_test mypy_benchmark mypy_script
-.PHONY: mypy_ci
 
+.PHONY: pytest_and_coverage #  Launch pytest and its coverage check
 pytest_and_coverage: pytest coverage
-.PHONY: pytest_and_coverage
 
+.PHONY: coverage # Check the coverage of code (within pytest)
 coverage:
 	@if [[ "$$BB" == "" ]]; then BB=origin/main; fi && \
 	poetry run diff-cover coverage.xml --fail-under 100 \
 	--html-report coverage.html --compare-branch $$BB
-.PHONY: coverage
 
+.PHONY: docker_build # Build dev docker
 docker_build:
 	docker build --pull -t $(DEV_DOCKER_IMG) -f $(DEV_DOCKERFILE) .
-.PHONY: docker_build
 
+.PHONY: docker_rebuild # Rebuild docker
 docker_rebuild:
 	docker build --pull --no-cache -t $(DEV_DOCKER_IMG) -f $(DEV_DOCKERFILE) .
-.PHONY: docker_rebuild
 
+.PHONY: docker_start # Launch docker
 docker_start:
 	@# the slash before pwd is for Windows
 	docker run --rm -it \
@@ -166,22 +169,22 @@ docker_start:
 	--volume $(DEV_CONTAINER_VENV_VOLUME):/root/dev_venv \
 	--volume $(DEV_CONTAINER_CACHE_VOLUME):/root/.cache \
 	$(DEV_DOCKER_IMG)
-.PHONY: docker_start
 
+.PHONY: docker_build_and_start # Docker build and start
 docker_build_and_start: docker_build docker_start
-.PHONY: docker_build_and_start
 
+.PHONY: docker_bas  # Docker build and start
 docker_bas: docker_build_and_start
-.PHONY: docker_bas
 
+.PHONY: docker_clean_volumes  # Docker clean volumes
 docker_clean_volumes:
 	docker volume rm -f $(DEV_CONTAINER_VENV_VOLUME)
 	docker volume rm -f $(DEV_CONTAINER_CACHE_VOLUME)
-.PHONY: docker_clean_volumes
 
+.PHONY: docker_cv # Docker clean volumes
 docker_cv: docker_clean_volumes
-.PHONY: docker_cv
 
+.PHONY: docker_publish_measurements # Run benchmarks in docker and publish results
 docker_publish_measurements: docker_build
 	mkdir -p .benchmarks
 	@# Poetry is not installed on the benchmark servers
@@ -189,80 +192,79 @@ docker_publish_measurements: docker_build
 	python script/progress_tracker_utils/extract_machine_info.py
 	docker run --rm --volume /"$$(pwd)":/src $(DEV_DOCKER_IMG) \
 	/bin/bash ./script/progress_tracker_utils/benchmark_and_publish_findings_in_docker.sh
-.PHONY: docker_publish_measurements
 
+.PHONY: docs # Build docs
 docs: clean_docs supported_functions
 	@# Generate the auto summary of documentations
 	poetry run sphinx-apidoc -o docs/_apidoc $(SRC_DIR)
-
 	@# Docs
 	cd docs && poetry run $(MAKE) html SPHINXOPTS='-W --keep-going'
-.PHONY: docs
 
+.PHONY: clean_docs # Clean docs build directory
 clean_docs:
 	rm -rf docs/_apidoc docs/_build
-.PHONY: clean_docs
 
+.PHONY: open_docs # Launch docs in a browser (macOS only)
 open_docs:
 	@# This is macOS only. On other systems, one would use `start` or `xdg-open`
 	open docs/_build/html/index.html
-.PHONY: open_docs
 
+.PHONY: build_and_open_docs # Build HTML docs and open it in a browser (macOS only)
 build_and_open_docs: clean_docs docs open_docs
-.PHONY: build_and_open_docs
 
+.PHONY: pydocstyle # Launch syntax checker on source code documentation
 pydocstyle:
 	@# From http://www.pydocstyle.org/en/stable/error_codes.html
 	poetry run pydocstyle $(SRC_DIR) --convention google --add-ignore=D1,D202 --add-select=D401
-.PHONY: pydocstyle
 
+.PHONY: finalize_nb # Sanitize notebooks
 finalize_nb:
 	poetry run python ./script/nbmake_utils/notebook_finalize.py $(NOTEBOOKS_DIR)
-.PHONY: finalize_nb
 
 # A warning in a package unrelated to the project made pytest fail with notebooks
 # Run notebook tests without warnings as sources are already tested with warnings treated as errors
+.PHONY: pytest_nb # Launch notebook tests
 pytest_nb:
 	poetry run pytest -Wignore --nbmake $(NOTEBOOKS_DIR)/*.ipynb
-.PHONY: pytest_nb
 
+.PHONY: benchmark # Launch benchmark
 benchmark:
 	poetry run python script/progress_tracker_utils/extract_machine_info.py
 	poetry run python script/progress_tracker_utils/measure.py benchmarks
-.PHONY: benchmark
 
+.PHONY: jupyter # Launch jupyter notebook
 jupyter:
 	poetry run jupyter notebook --allow-root --no-browser --ip=0.0.0.0
-.PHONY: jupyter
 
+.PHONY: release_docker # Build a docker release image
 release_docker:
 	./docker/build_release_image.sh
-.PHONY: release_docker
 
+.PHONY: upgrade_py_deps # Upgrade python dependencies
 upgrade_py_deps:
 	./script/make_utils/upgrade_deps.sh
-.PHONY: upgrade_py_deps
 
 # This is done by hand as pytest-codeblocks was failing with our native extensions.
 # See refused PR on the project here: https://github.com/nschloe/pytest-codeblocks/pull/58
+.PHONY: test_codeblocks # Test code block in the documentation
 test_codeblocks:
 	poetry run python ./script/make_utils/test_md_python_code.py --md_dir docs/
-.PHONY: test_codeblocks
 
 # From https://stackoverflow.com/a/63523300 for the find command
+.PHONY: shell_lint # Lint all bash scripts
 shell_lint:
 	find \( -path "./.venv" -o -path "./.docker_venv" \) -prune -o -type f -name "*.sh" -print | \
 	xargs shellcheck
-.PHONY: shell_lint
 
+.PHONY: set_version_no_commit # Dry run for set_version
 set_version_no_commit:
 	@if [[ "$$VERSION" == "" ]]; then											\
 		echo "VERSION env variable is empty. Please set to desired version.";	\
 		exit 1;																	\
 	fi && \
 	poetry run python ./script/make_utils/version_utils.py set-version --version "$${VERSION}"
-.PHONY: set_version_no_commit
 
+.PHONY: set_version # Generate a new version number and update all files with it accordingly
 set_version:
 	@if [[ "$$VERSION" == "" ]]; then											\
 		echo "VERSION env variable is empty. Please set to desired version.";	\
@@ -277,18 +279,18 @@ set_version:
 	if [[ "$$NEW_STASH_COUNT" != "$$STASH_COUNT" ]]; then \
 		git stash pop; \
 	fi
-.PHONY: set_version
 
+.PHONY: check_version_coherence # Check that all files containing version have the same value
 check_version_coherence:
 	poetry run python ./script/make_utils/version_utils.py check-version
-.PHONY: check_version_coherence
 
+.PHONY: changelog # Generate a changelog
 changelog: check_version_coherence
 	PROJECT_VER=($$(poetry version)) && \
 	PROJECT_VER="$${PROJECT_VER[1]}" && \
 	poetry run python ./script/make_utils/changelog_helper.py > "CHANGELOG_$${PROJECT_VER}.md"
-.PHONY: changelog
 
+.PHONY: release # Create a new release
 release: check_version_coherence
 	@PROJECT_VER=($$(poetry version)) && \
 	PROJECT_VER="$${PROJECT_VER[1]}" && \
@@ -296,39 +298,39 @@ release: check_version_coherence
 	git fetch --tags --force && \
 	git tag -s -a -m "$${TAG_NAME} release" "$${TAG_NAME}" && \
 	git push origin "refs/tags/$${TAG_NAME}"
-.PHONY: release
 
-# Show the accepted types and optional scopes
+
+.PHONY: show_scope # Show the accepted types and optional scopes (for git conventional commits)
 show_scope:
 	@echo "Accepted types and optional scopes:"
 	@cat .github/workflows/continuous-integration.yaml | grep feat | grep pattern | cut -f 2- -d ":" | cut -f 2- -d " "
-.PHONY: show_scope
 
+.PHONY: show_type # Show the accepted types and optional scopes (for git conventional commits)
 show_type:show_scope
-.PHONY: show_type
 
 # grep recursively, ignore binary files, print file line, print file name
 # exclude dot dirs, exclude pylintrc (would match the notes)
 # exclude notebooks (sometimes matches in svg text), match the notes in this directory
+.PHONY: todo # List all todo left in the code
 todo:
 	@NOTES_ARGS=$$(poetry run python ./script/make_utils/get_pylintrc_notes.py \
 	--pylintrc-path pylintrc) && \
 	grep -rInH --exclude-dir='.[^.]*' --exclude=pylintrc --exclude='*.ipynb' "$${NOTES_ARGS}" .
-.PHONY: todo
 
-# Update docs with supported functions
+
+.PHONY: supported_functions # Update docs with supported functions
 supported_functions:
 	poetry run python script/doc_utils/gen_supported_ufuncs.py docs/user/tutorial/WORKING_WITH_FLOATING_POINTS.md
-.PHONY: supported_functions
 
+.PHONY: check_supported_functions # Check supported functions (for the doc)
 check_supported_functions:
 	poetry run python script/doc_utils/gen_supported_ufuncs.py docs/user/tutorial/WORKING_WITH_FLOATING_POINTS.md --check
-.PHONY: check_supported_functions
 
+.PHONY: licences # Generate the list of licenses of dependencies
 licences:
 	@./script/make_utils/licences.sh
-.PHONY: licences
 
+.PHONY: check_licences # Check if the licenses of dependencies have changed
 check_licences:
 	@TMP_OUT="$$(mktemp)" && \
 	if ! ./script/make_utils/licences.sh --check > "$${TMP_OUT}"; then \
@@ -341,3 +343,6 @@ check_licences:
 	fi
 .PHONY: check_licences
 
+.PHONY: help # Generate list of targets with descriptions
+help:
+	@grep '^.PHONY: .* #' Makefile | sed 's/\.PHONY: \(.*\) # \(.*\)/\1\t\2/' | expand -t30 | sort