Data mining is a process of discovering hidden relationships in large amounts of data. Frequent pattern discovery is an important research area in the field of data mining. Its purpose is to find patterns which appear frequently in a large collection of data. This work deals with three main areas of frequent pattern mining, namely, frequent itemset, frequent sequence and frequent subtree discovery. Beside providing a brief overview of related works of each single frequent pattern mining problem mentioned before, the three theses offered in this work suggest novel methods for efficient discovery of the different types of frequent patterns. The new methods are compared to the best-known algorithms in the related fields. The performance analysis of the methods involves measurements of the execution time and memory requirements.