The area of interest in this thesis is algebraic combinatorics. The focus is directed towards the analysis of Young's lattice, that is, the set of partitions of natural numbers together with the corresponding partial order. In the thesis, Young's diagrams which represent partitions of natural numbers are presented and special subsets of the set of partitions and their properties are studied. Using the concept of \(q\)-binomial coefficients, some properties of Young's lattice are investigated. Numerous properties and recursive relations for \(q\)-binomial coefficients are discussed, including symmetry and unimodality, and many combinatorial interpretations of \(q\)-binomial coefficients are given. Also, Hasse walks in Young's lattice are discussed. The importance of Hasse walks lies in the fact that the set of all permutations of a finite set is equipotent with a specific subset of the set of Hasse walks. A concept related are Young tableaus, an important tool in the representation theory of the symmetric group. The thesis also gives a description of the RSK algorithm that establishes a bijection between permutations of a finite set and pairs of standard Young tableau of the same form.