Theoretical Study on Correlation Effects in Topological Matter Introduction Interacting Dirac fermions in (3+1) dimensions Tilted Dirac cones in two dimensions Generalized Hunds rule for two atom systems Interacting topological crystalline insulators Conclusions and prospects. This thesis elucidates electron correlation effects in topological matter whose electronic states hold nontrivial topological properties robust against small perturbations. In addition to a comprehensive introduction to topological matter this thesis provides a new perspective on correlated topological matter. The book comprises three subjects in which electron correlations in different forms are considered. The first focuses on Coulomb interactions for massless Dirac fermions. Using a perturbative approach the author reveals emergent Lorentz invariance in a low energy limit and discusses how to probe the Lorentz invariance experimentally. The second subject aims to show a principle for synthesizing topological insulators with common light elements. The interplay between the spin–orbit interaction and electron correlation is considered and Hunds rule and electron filling are consequently found to play a key role for a strong spin–orbit interaction important for topological insulators. The last subject is classification of topological crystalline insulators in the presence of electron correlation. Unlike non interacting topological insulators such two and three dimensional correlated insulators with mirror symmetry are demonstrated to be characterized respectively by the Z4 and Z8 group by using the bosonization technique and a geometrical consideration.