If you are new to critical rationalism and wondering what to read, I’ll offer some personal suggestions.
You can’t go wrong reading Karl Popper. If you are primarily interested in Popper’s views on science, Conjectures and Refutations is a much better starting point than The Logic of Scientific Discovery. If you are primarily interested in Popper’s overall philosophy and his political views, start with The Open Society and Its Enemies. If you are interested in Popper at his metaphysical best, then Objective Knowledge is a truly wonderful book. I’ve never been disappointed in any book I’ve read by Popper.
Also worth nothing here is the excellent Popular Popper series by Rafe Champion. These are study guides that are intended to assist people reading Popper’s books. They clarify the main issues at stake in each book and provide a lot of important context. For people trying to understand Popper’s books, they can be very helpful.
There are many other writers to read. One of my favorite books is by W.W. Bartley III, The Retreat to Commitment. This book is more far reaching than its topic, modern Protestant theology, would suggest. The book questions the manner in which we all present arguments and makes some startling discoveries. A truly excellent book. Make sure to read the second edition!
Beyond this, there are so many good books to read, I find it hard to know where to begin. Below I’ll offer links to some helpful lists.
Note: Additions and corrections are not only welcome but hoped for, please comment!