The h-principle is a powerful tool in differential topology which is used to study spaces of functions
with certain distinguished properties (immersions, submersions, k-mersions, embeddings, free maps, etc.). I
will discuss some examples of the h-principle and give a neat proof of a special case of the Smale-Hirsch
Theorem, using the "removal of singularities" h-principle technique due to Eliashberg and Gromov. Finally, I will
define and discuss totally convex immersions and discuss some h-principle statements in this context.