In this thesis, we study Pick’s formula, a formula that connects problems from two entirely different realms of mathematics - counting problems from discrete mathematics and problem of calculating area from geometry. In the first chapter, we provide definitions, theorems, and results from geometry and discrete mathematics that are necessary for understanding the main part of the thesis. In the second chapter, we examine the problems that lead us to Pick’s formula. In the third chapter, two proofs of Pick’s formula are presented, relying on elementary geometric concepts and results. Next, in the fourth chapter, we explore extensions of Pick’s formula and investigate the relationship between Pick’s formula and homothety. The fifth chapter presents the general lattice theory which, as a consequence of certain more general results, leads us to Pick’s formula as well. The thesis concludes with the sixth chapter, which discusses a methodical approach to introducing Pick’s formula in elementary education.