This thesis focuses on \(p\)-adic numbers and provides a sort of an introduction to the \(p\)-adic analysis. Its main goal is to define the field of \(p\)-adic numbers \(\mathbb{Q}_p\) and lay the foundation for introduction of the \(p\)-adic analogue of the set of complex numbers \(\mathbb{C}\). The paper is divided into three chapters. We begin the first chapter by recalling the concepts of fields, metrics, norms, and metric spaces. Then we introduce a new type of distance that we will deal with throughout the rest of the paper, namely \(p\)-adic distance. We also distinguish norms depending on whether they are Archimedean or non-Archimedean. We define equivalent norms and metrics, prove their various properties and mention the Ostrowski theorem. Then we recall the construction of complex numbers and in a similar way we construct the field of \(p\)-adic numbers \(\mathbb{Q}_p\). In the rest of the chapter we study its arithmetic and prove the important Hensel lemma. In the second chapter we study the Riemann \(\zeta\) function and its \(p\)-adic interpolation. We start by defining the Bernoulli numbers \(B_k\) that appear in the formula for\(\zeta(2k)\), which we then prove. Furthermore, we observe the topology on \(\mathbb{Q}_p\) and introduce compactopen sets and locally constant functions. We then use them in the definition of \(p\)-adic distributions and give a few examples. We also touch on Bernoulli polynomials \(B_k(x) \) and Bernoulli distributions, and introduce measures and integration in \(\mathbb{Q}_p\). Using the introduced distributions and expressions for \(\zeta(2k)\), we define \(p\)-adic interpolations of the \(\zeta\)-function. In the third chapter we talk about the gamma function. We give its definition and proof of its basic properties. In doing so, we recall some concepts from the field of complex analysis such as analytical functions, poles and residues. We conclude the chapter by using the gamma function in proving the infinite product identity for hyperbolic sine that was mentioned in the second chapter.