TITLE: Type Theory for Beginners
QUESTION [11 upvotes]: One of the first things one learns at university are some foundations of mathematics. This covers topics such as sets, functions between sets, relations, logic & proof, ...
I learned this stuff too. But it does not satisfy me because some things seem to be too unnatural for me. In this blog post, Dr. Shulman explains that these problems with the "standard" foundations (ZFC, ETCS) are solved by type theory.
The standard reference to learn type theory is the Homotopy Type Theory book. But this book is too complicated for me, since I am a beginner. That is why I am searching for material from which I can learn type theory. This material should be written for the same audience for which the introductions to sets, functions, ... mentioned above are written.

REPLY [2 votes]: I'd suggest "Type theory and functional programming" by Simon Thompson. It's a bit older, but it gives a much gentler overview of type theory than the HoTT book. In contrast to Pierce's TAPL, it handles the full version of dependent type theory rather than the more limited theories such as F_omega. It's freely available from https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/.
Alternatively, if you want a more practical introduction to the subject then I recommend the recent book "Verified functional programming in Agda" by Aaron Stump. It is very accessible to newcomers yet it builds up to some impressive applications of type theory.