Microbial communities are an integral and indispensable part of biogeochemical processes, health of plants and animals, and human activities [1-3]. The community structure (the members and their relative abundance) is a key variable that determines the dynamics, stability, functions, and evolution of a microbial community [4]. However, our capability of interpreting, predicting, and controlling microbial community structure is still lacking. This is manifested in the challenges we face in maintaining the stable colonization of beneficial strains [5], reducing the colonization of pathogenic strains [6], and controlling the community structure for engineering purposes [7]. To solve this problem, one approach is to develop methods and tools specific to each system. However, due to the diversity and complexity of microbial communities, these system-specific approaches can be labor intensive and ad hoc. The opposite approach is to distill general principles that can be widely applicable to any microbial communities without characterizing low-level details, such as at the metabolic level. If there exist such general rules, we can then build a toolbox to solve classes of problems related to microbial community structure in an efficient manner. In this dissertation, I lay out the reasoning and steps to distill general principles that underlie microbial community structure. Using this approach, I then study two types of factors that have significant impacts on microbial community structures. One is a study on mutualism, where I established a general mathematical criterion that underlies the coexistence of mutualistic systems and developed a machine learning method to apply the criterion to diverse experimental systems for interpretation and prediction of system outcomes. The other study is on spatial partitioning, where I established that spatial partitioning increases biodiversity for communities dominated by negative interactions and decreases biodiversity for those dominated by positive interactions. When strong ...