diff --git a/doc/Makefile b/doc/Makefile
index ce8dc86f764..52f816f8ad0 100644
--- a/doc/Makefile
+++ b/doc/Makefile
@@ -7,29 +7,25 @@ SPHINXAUTOGEN = sphinx-autogen
 BUILDDIR      = _build
 
 # Internal variables.
-ALLSPHINXOPTS   = -d $(BUILDDIR)/doctrees  $(SPHINXOPTS) .
+ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees  $(SPHINXOPTS) .
 
-.PHONY: help clean html linkcheck doctest api
-
-all: html
+.PHONY: help all api html server clean
 
 help:
-	@echo "Please use \`make <target>' where <target> is one of"
-	@echo "  all        generate the complete webpage"
-	@echo "  html       make only the HTML files from the existing rst sources"
-	@echo "  linkcheck  check all external links for integrity"
-	@echo "  doctest    run all doctests embedded in the documentation (if enabled)"
+	@echo "Please use 'make <target>' where <target> is one of"
+	@echo "  all        build the HTML files from the existing rst sources"
+	@echo "  api        generate rst source files of API documentation"
+	@echo "  html       build the HTML files from the existing rst sources"
+	@echo "  server     make a local HTTP server for previewing the built documentation"
+	@echo "  clean      clean up built and generated files"
 
-clean:
-	rm -rf $(BUILDDIR)/html
-	rm -rf $(BUILDDIR)/doctrees
-	rm -rf $(BUILDDIR)/linkcheck
-	rm -rf modules
-	rm -rf api/generated
-	rm -rf gallery
-	rm -rf tutorials
-	rm -rf projections
-	rm -rf .ipynb_checkpoints
+all: html
+
+api:
+	@echo
+	@echo "Generating rst source files of API documentation."
+	@echo
+	$(SPHINXAUTOGEN) -i -t _templates -o api/generated api/*.rst
 
 html: api
 	@echo
@@ -39,23 +35,16 @@ html: api
 	@echo
 	@echo "Build finished. The HTML pages are in $(BUILDDIR)/html."
 
-api:
+server:
 	@echo
-	@echo "Building API docs."
+	@echo "Running a server on port 8009."
+	@echo "Open http://localhost:8009 in a web browser to preview the documentation."
 	@echo
-	$(SPHINXAUTOGEN) -i -t _templates -o api/generated api/*.rst
-
-
-linkcheck:
-	$(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
-	@echo
-	@echo "Link check complete; look for any errors in the above output " \
-	      "or in $(BUILDDIR)/linkcheck/output.txt."
-
-doctest:
-	$(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
-	@echo "Testing of doctests in the sources finished, look at the " \
-	      "results in $(BUILDDIR)/doctest/output.txt."
-
-serve:
 	cd $(BUILDDIR)/html && python -m http.server 8009
+
+clean:
+	rm -rf $(BUILDDIR)
+	rm -rf api/generated
+	rm -rf gallery
+	rm -rf tutorials
+	rm -rf projections