The spectral theory studies the spectral properties of graphs and their relation to the combinatorics properties of graph. Central to this rich theory, the Cheeger's inequality bounds the expansion or conductance of the graph by the second least eigenvalue of the Laplacian of the graph. Recently, the Cheeger's inequality was generalized to the case of hypergraph with notions of hypergraph expansion and hypergraph Laplacian. This project will mostly be concerned with the study of the spectral properties of this hypergraph Laplacian, from both a mathematical and algorithmatic point of view.