In calculus, we integrate functions using two types of integration -- definite integration and indefinite integration. In functional analysis, we integrate operators. To find a solution of a differential equation, we integrate this equation. Going beyond mathematics, we see that in databases, we integrate data, as well as database schemas. In electronics, integrated circuits have become central components of computers, calculators, cellular phones, and other digital appliances, which are now inextricable parts of the structure of modern societies. In economics, we have integration of the economy of one country into the economy of a union of other countries, eg: integration of economy of Hungary into the European Union economy. There is political integration and there is social integration. Thus, we can see many types and kinds of integration. Design of complex database schemas is based on a gradual integration of external schemas. Research presented in this book studies integration in mathematics and its applications. However, it is not only classical integration of functions but also fuzzy integration, integration of structures, probability as integration of random characteristics and integral operators in bundles with a hyperspace base.