diff --git a/README.rst b/README.rst
index c563e78bbdcd70a8978f4a5ea6b25f9ce11ab2ad..4c5e8e14b407e2b4cab54dc75de96ec9295544d1 100644
--- a/README.rst
+++ b/README.rst
@@ -15,11 +15,11 @@ PyOpenCL: Pythonic Access to OpenCL, with Arrays and Algorithms
 
 PyOpenCL lets you access GPUs and other massively parallel compute
 devices from Python. It tries to offer computing goodness in the
-spirit of its sister project `PyCUDA <http://mathema.tician.de/software/pycuda>`_:
+spirit of its sister project `PyCUDA <https://mathema.tician.de/software/pycuda>`_:
 
 * Object cleanup tied to lifetime of objects. This idiom, often
   called
-  `RAII <http://en.wikipedia.org/wiki/Resource_Acquisition_Is_Initialization>`_
+  `RAII <https://en.wikipedia.org/wiki/Resource_Acquisition_Is_Initialization>`_
   in C++, makes it much easier to write correct, leak- and
   crash-free code.
 
@@ -33,11 +33,11 @@ spirit of its sister project `PyCUDA <http://mathema.tician.de/software/pycuda>`
 * Speed. PyOpenCL's base layer is written in C++, so all the niceties
   above are virtually free.
 
-* Helpful and complete `Documentation <http://documen.tician.de/pyopencl>`__
+* Helpful and complete `Documentation <https://documen.tician.de/pyopencl>`__
   as well as a `Wiki <http://wiki.tiker.net/PyOpenCL>`_.
 
 * Liberal license. PyOpenCL is open-source under the 
-  `MIT license <http://en.wikipedia.org/wiki/MIT_License>`_
+  `MIT license <https://en.wikipedia.org/wiki/MIT_License>`_
   and free for commercial, academic, and private use.
 
 * Broad support. PyOpenCL was tested and works with Apple's, AMD's, and Nvidia's 
@@ -52,15 +52,15 @@ instead build from source:
 
 *   gcc/g++ new enough to be compatible with pybind11
     (see their `FAQ <https://pybind11.readthedocs.io/en/stable/faq.html>`_)
-*   `numpy <http://numpy.org>`_, and
+*   `numpy <https://numpy.org>`_, and
 *   an OpenCL implementation. (See this `howto <http://wiki.tiker.net/OpenCLHowTo>`_ for how to get one.)
 
 Places on the web related to PyOpenCL:
 
-* `Python package index <http://pypi.python.org/pypi/pyopencl>`_ (download releases)
+* `Python package index <https://pypi.python.org/pypi/pyopencl>`_ (download releases)
 
-* `Documentation <http://documen.tician.de/pyopencl>`__ (read how things work)
+* `Documentation <https://documen.tician.de/pyopencl>`__ (read how things work)
 * `Conda Forge <https://anaconda.org/conda-forge/pyopencl>`_ (download binary packages for Linux, macOS, Windows)
 * `C. Gohlke's Windows binaries <http://www.lfd.uci.edu/~gohlke/pythonlibs/#pyopencl>`_ (download Windows binaries)
-* `Github <http://github.com/inducer/pyopencl>`_ (get latest source code, file bugs)
+* `Github <https://github.com/inducer/pyopencl>`_ (get latest source code, file bugs)
 * `Wiki <http://wiki.tiker.net/PyOpenCL>`_ (read installation tips, get examples, read FAQ)