In the master's thesis we present the homology of a body or surface. Homology helps us recognize, count and measure different types of "holes" in space, such as gaps, loops or cavities. The main focus of the work is on the theoretical background and on the definition of homology which is defined through vector spaces. We presented a few examples of homology calculations and wrote a program code that calculates the dimension of homology vector spaces for any triangulated body or surface. The final part of the thesis presents applications where homological methods are used. For example, with the help of homology, we can detect holes in wireless networks, and it also aids us in the detection of cancerous tissues.
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