This chapter contains a general notion of random processes with continuous time. It is given in context of the Kolmogorov consistency theorem. The notion of a Wiener process with a variety of its properties is also presented here. Its existence is stated by two ways: with the help of the Kolmogorov theorem as well as with the help of orthogonal functional systems. Besides the Wiener process as a basic process for many others, the Poisson process is also considered here. Stochastic integration with respect to wiener process is developed for a class of progressively measurable functions. It leads to the Ito processes, the Ito formula, the Girsanov theorem, and representation of martingales (see Borodin, Stochastic processes, 2018; Bulinski and Shiryayev, Theory of stochastic processes, 2005; Ikeda and Watanabe, Stochastic differential equations and diffusion processes, 2nd edn., 1989; Karatzas and Shreve, Brownian motion and stochastic calculus, 1998; Krylov, Introduction to the theory of random processes, 2002; Øksendal, Stochastic differential equations, 5th edn., 2000; Skorokhod, Lectures on the theory of stochastic processes, 1996, and Wentzell, A course in the theory of stochastic processes, 1981).