-Duration: 12 hours -Schedule: from 14 May to 4 June 2026, every Tuesday and Thursday (except 2 June), at 11:00-13:00, at the University of Tor Vergata. All lectures will take place in Room Dal Passo except for the first class on 14 May which will be in Room D'Antoni. The schedule can be modified according to the availability of those interested. -Abstract: This minicourse provides an introduction to topological methods in dynamical systems, with an emphasis on Conley Index Theory. Conley theory can be viewed as a far-reaching generalization of Morse theory, extending its applicability beyond gradient-like dynamics. We begin by reviewing the main concepts and results of classical Morse theory, highlighting its role in understanding the topology of manifolds through the critical points of smooth functions. We then introduce the fundamental definitions and key properties of the Conley index, emphasizing its robustness and flexibility in the study of general dynamical systems. Finally, we discuss Morse decompositions and their associated Morse–Conley inequalities, illustrating how these tools provide deep insights into the structure of invariant sets and the qualitative behaviour of flows.