Abstract: In these two seminars, I will review Furstenberg's theory for the top Lyapunov exponent of products of i.i.d. random matrices. Furstenberg's approach to the problem relies on the study of certain Markov processes on the projective space. The material presented is based on the papers: H. Furstenberg, Noncommuting random products, Trans. Amer. Math. Soc. 108 (1963) 366-428, and H. Furstenberg & Y. Kifer, Random matrix products and measures on projective spaces, Israel J. of Math. 46 (1983) 12-32.