The thesis String similarity measures examines string matching problem, where we are interested in matchings allowing errors. Such problem is also called approximate string matching problem, and its essential part is the definition of error model and by this the type of a similarity or dissimilarity measure. In the beginning of the thesis we present a general overview of measures, then we further focus on the group of measures based on the edit operations on strings. The definition of such distance between strings is established with the cost of operations that are needed for an optimal transformation from one string to another. Further on, we describe a few algorithms based on dynamic programming, and then we add a couple of upgraded versions. With a help of an example we try to demonstrate their performance and analyse their computational complexity.