This PhD dissertation by László Varga, supervised by András Zempléni, focuses on the computational aspects of bootstrap methods in theoretical and applied statistics. The dissertation aims to outline the basic concepts of bootstrap methods, address mathematical challenges, expand the theory with new methods, and demonstrate their practical applications. The dissertation is structured into several chapters: 1. **Introduction**: Provides an overview of the author's background, the motivation for the research, and the structure of the dissertation. 2. **Special Topics from Probability Theory and Statistics**: Covers essential concepts from probability theory, time series analysis, extreme value theory, and copula theory. It includes results on random sums, convergence of random variables, stationary time series models, and extreme value distributions. 3. **Bootstrap Methods**: Summarizes the theory of bootstrap, including the principle of bootstrapping, limitations of the classical i.i.d. bootstrap, block bootstrap methods, and weighted bootstrap. It also discusses practical issues such as block size determination, copula goodness-of-fit testing, and profile likelihood. 4. **Applications**: presents three practical applications of the generalized block bootstrap and weighted likelihood bootstrap. These applications include modeling wind speed, precipitation, and temperature data, with a focus on climate change analysis. The dissertation includes detailed proofs for several key results and uses R programming for simulations and data analysis. It highlights the importance of understanding the theoretical foundations and practical implementation of bootstrap methods in various statistical contexts.This PhD dissertation by László Varga, supervised by András Zempléni, focuses on the computational aspects of bootstrap methods in theoretical and applied statistics. The dissertation aims to outline the basic concepts of bootstrap methods, address mathematical challenges, expand the theory with new methods, and demonstrate their practical applications. The dissertation is structured into several chapters: 1. **Introduction**: Provides an overview of the author's background, the motivation for the research, and the structure of the dissertation. 2. **Special Topics from Probability Theory and Statistics**: Covers essential concepts from probability theory, time series analysis, extreme value theory, and copula theory. It includes results on random sums, convergence of random variables, stationary time series models, and extreme value distributions. 3. **Bootstrap Methods**: Summarizes the theory of bootstrap, including the principle of bootstrapping, limitations of the classical i.i.d. bootstrap, block bootstrap methods, and weighted bootstrap. It also discusses practical issues such as block size determination, copula goodness-of-fit testing, and profile likelihood. 4. **Applications**: presents three practical applications of the generalized block bootstrap and weighted likelihood bootstrap. These applications include modeling wind speed, precipitation, and temperature data, with a focus on climate change analysis. The dissertation includes detailed proofs for several key results and uses R programming for simulations and data analysis. It highlights the importance of understanding the theoretical foundations and practical implementation of bootstrap methods in various statistical contexts.