In this chapter, we explain p-adic calculus for functions whose arguments and values are p-adic numbers, especially when the domain of the functions is \(\mathbb Z_p^n\) , the n-th Cartesian power of \(\mathbb Z_p\) , and the functions take values in \(\mathbb Z_p^m\) , for some \(n,m\in \mathbb N=\{1,2,3,\ldots \}\) , (usually \(m\leqslant n\) ). Though general p-adic calculus can be found in a number of respective books that are mentioned earlier (in Chap. 2 ), in the current chapter, we are mostly focused on the main object of our investigation, the p-adic 1-Lipschitz functions, since the latter functions can be treated as causal functions over discrete time. This is why we give only references where the proofs of general results of p-adic calculus can be found and prove only the results that are specific for the theme of the book. Therefore, this chapter should not be judged as a crash course of p-adic calculus; there are much better books for a novice (see, e.g., (Katok, p-adic Analysis in Comparison with Real, Mass. Selecta. American Mathematical Society (2003); Mahler, p-adic Numbers and their Functions, 2nd edn., Cambridge Univ. Press (1981); Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-functions, Graduate Texts in Math., vol. 58, 2nd edn., Springer-Verlag (1984))).