I need to devise a module for next academic year which is an introduction to pure mathematics. They need to use this module as a step stone module such as number theory, group theory, combinatorics, and real analysis.

What should I cover to make this interesting and be used as a hook for them to be motivated to do pure mathematics? Should have an impact on them.

It will be a first-year university undergraduate module.

This would be a good course textbook for you.

The Foundations of Mathematics Paperback  (2015)

Stewart and Tall.