In this thesis we have presented the red-black tree as a type of binary search tree with good balance. In the first chapter we have given the definition of red-black trees and listed red-black properties that such tree must satisfy. We have shown that these properties ensure that no path from the root to a leaf is not more than two times longer than any other path from the root to a leaf and proved that therefore such tree with \(n\) nodes has a height of \(O(\log {n})\). In the next chapter we have dealt with the operations of the red-black tree. We have not described search operation because it is similar to that of a general tree. We have described and analyzed the duration of the rotation that has been most often used to "repair" the red-black tree, along with changing colors. We have put more emphasis on insertion and deletion. Both operations are based on the same operations defined for generally binary tree, but we have seen that they can violate the properties of red-black tree. We have presented these cases with sketches and described how to solve them. We have also given pseudocode for these operations and analyzed their time complexity. In the last chapter we have described the project Red Black Trees that was made as part of this work and that implements the solution of one geometric problem with red-black tree. We have explained how to run and use the project, and we have given and described parts of implementation.