Introduction to the hprinciple
In 2019, I teach a graduate course about the hprinciple in
M2
AAG.
Main references are:
 EliashbergMishachev's book Introduction to the hprinciple
 Any lecture note from
Vincent Borrelli.
 Gromov's book Partial differential relations (hard)
There are
lectures notes.
Student talks suggestions
In the following list, EM means EliashbergMishchev's book. The first
three items are directly in line with the lectures. The last two are
much more ambitious, but giving an idea of how ideas from the lectures
can be complemented with other ideas would already be nice.

Isosymplectic embeddings
EM Thm 12.1.1. Holonomic approximation and symplectic geometry.

Holonomic approximation for microflexible relations
EM chapter 13 (aim for Thm 13.4.1, bonus 16.1.2). Variation on proof
of holonomic approximation.

First order differential operators
EM Chap 20. Convex integration for operators like divergence.

René Thom and the hprinciple
Discuss how this paper
proves existence of sphere eversion following ideas from Thom.

Convex integration ans PDEs
Discuss this survey.

Positive isotopies of loose Legendrians
Main result from this paper.

Legendriennes lâches et plastikstufe
Theorem 1.1 from this paper.

Existence of contact structures in higher dimensions
Discuss something of the main proof of
this paper
One more reasonnable goal could be explaining existence on closed
3manifold from this point of view. See also
this Bourbaki talk and references quoted at the end of
introduction.

Topological characterization of Stein manifolds
Thm 1.5 from
this survey
(see also Cieliebak and Eliashberg book if needed).