This chapter is dedicated to the simple symmetric random walk on the integers. Such a random walk can be represented as a path in a coordinate system. For random walks of a given length, we examine the time of the last zero-crossing, the number of zero-crossings, sojourn times above the x-axis, the maximum and minimum values, the number and location of maxima, changes of sign, and the absolute maximum, with an application to a symmetry test. As the length increases, many surprising limit theorems emerge, such as the arcsine law for the time of the last zero-crossing and the sojourn time. Other topics include first return time and recurrence, first-passage times and first-passage epochs, intersections of random walks, and duality. The chapter concludes with an outlook on the Brownian motion (Wiener process).