The theme of this book is the spectral properties of graphs. The book is divided into four chapters. Chapter 1 presents some basic terminologies and notations. Chapter 2 devotes to hyperenergetic graphs and the largest eigenvalue of non-regular graphs associated with the spectrum of graphs. Chapter 3 provides some results on the Laplacian spectrum of graphs, included Laplacian spread, Laplacian spectral ratio, Laplacian-energy-like, Kirchhoff index and the sum of Laplacian eigenvalues. The separator, spread and spectral radius on signless Laplacian spectrum of graphs are studied in Chapter 4.