Our concern is the study of linear equations with quasi-periodic coefficients, which appear in many concepts. As a typical example, the well known Schrödinger equations with quasi-periodic potentials can be rewritten as quasi-periodic cocycles. The most common way to understand the behavior of such systems is by studying their stability, which we call reducibility.
I will first give an introduction to the concepts of quasi-periodic cocycles, reducibility and almost-reducibility. In a second part, we will discuss strategy to obtain perturbative almost-reducibility.