This undergraduate thesis task was to describe in detail, explain and compare most common and optimized algorithms for shortest path problem in graph with accent on their implementation and comparison in C++ programming language. Shortest path problem is base for different system implementations in computer science, network routing and logistics. Firstly, we introduce base concepts of graphs and shortest path problem, defining graphs, what are edges, weights, nodes, or vertices, directed and undirected graph and graph with positive and negative edge weights. After that we define principle and mathematical form how we represent graphs in computer science for easiest storing in memory and handling with them so we could implement them in programming language. With detailed description we define key algorithms for shortest path problem in graph, making detail implementation in C++ of every described algorithm, we compare their performance and test them with different data sets. This work is concluded with tips for choosing appropriate algorithm depending on system and problem needs. Firstly, we introduce base concepts of graphs and shortest path problem, defining graphs, what are edges, weights, nodes, or vertices, directed and undirected graph and graph with positive and negative edge weights. After that we define principle and mathematical form how we represent graphs in computer science for easiest storing in memory and handling with them so we could implement them in programming language. With detailed description we define key algorithms for shortest path problem in graph, making detail implementation in C++ of every described algorithm, we compare their performance and test them with different data sets. This work is concluded with tips for choosing appropriate algorithm depending on system and problem needs.