In 1968, G.-C. Rota introduced a notion of a Baxter operator and a Baxter algebra. These are the ultimate generalizations of the results of E.Sparre Andersen, H.F.Bohnenblust-F.Spitzer, G.Baxter, and others, in the fluctuation theory of sums of independent random variables. The characteristic function of the maximum of a random walk has been computed by Spitzer with the help of a combinatorial theorem due to Bohnenblust. The approach of Baxter uses a certain operator identity which inspired the Rota's work. We will try to explain the main result of Rota on Baxter algebras, that a standard Baxter algebra on any finite number of generators is free in the category of Baxter algebras. This result implies in particular (i) that the Baxter-Spitzer-Pollaczek formula holds in any Baxter algebra; (ii) the mentioned results in random walk theory; (iii) the Bohnenblust-Spitzer combinatorial theorem.