In this thesis we deal with the \(p\)-adic numbers, with the emphasis on equations with \(p\)-adic numbers. In the first chapter, we introduce the \(p\)-adic integers and \(p\)-adic numbers by looking at the analogy between the ring of integers, \(\mathbb{Z}\), together with the field of fractions \(\mathbb{Q}\) and the ring of polynomials with coefficients from a set of complex numbers, \(\mathbb{C}[X]\), together with the field of fractions of \(\mathbb{C}[X]\). Then in the next subsection we deal with the \(p\)-adic absolute value in which we prove a theorem and Ostrowski that connects each nontrivial absolute value of the field \(\mathbb{Q}\) and the \(p\)-adic absolute value. At the end of the first chapter we give a brief outline of "good" and "bad" properties of \(p\)-adic numbers by comparing them with rational numbers. In the second chapter, we first deal with calculations in \(\mathbb{Q}_p\). Special attention is given to the existence of square roots in the field \(\mathbb{Q}_p\). For us, this represent a slight introduction to the equation with \(p\)-adic numbers. After that we solve congruences modulo \(p^n\) whichare now sufficiently "close" to equations in \(p\)-adic numbers to considered them equations in \(p\)-adic numbers. Then we give some important results about solutions of equations in \(p\)-adic numbers with coefficients being \(p\)-adic integers. This was the aim of this work. The last chapter gives a brief summary in which is visible on application of \(p\)-adic numbers.