Many mathematical problems are solved by translating them into other, better-known and studied problems.
For this purpose, matrices are often used to compactly express the properties of certain objects.
This approach sometimes, in more or less surprising ways, leads to determinantal formulas.
This thesis presents several examples of the use of determinants and determinantal formulas in combinatorics.
The focus is on the formulation and proof of the Lindström-Gessel-Viennot lemma.
Its application is also demonstrated, particularly in the proof of the Binet-Cauchy theorem and the Jacobi-Trudi identity.
The aim is to present the reader with interesting cases where a translation to graph theory leads to an elegant solution.
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