Textbook in PDF format This book provides unique introduction for experimentalists to theoretically calculate vibrational (IR, Raman, SFG) spectra of molecules in liquid and solid phases. Vibrational spectroscopy is the most popular and valuable tool for scientists to obtain physicochemical insight into complex molecular systems. Although standard softwares of quantum chemistry calculations routinely provide predictions of spectra, this book describes dynamic aspects and spectroscopic accuracy enough to compare our experimental data directly to computations, that lack in the softwares. The quantum/classical mixed approach presented in this book allows researchers including graduate students of chemistry and physics to extract microscopic information of structure and dynamics from their vibrational spectroscopic experimental data with no help from theoreticians. Overview of Quantum/Classical Mixed Approach Construction of Vibrational Hamiltonian Computation of Spectra from Hamiltonian Application to Liquid Water Surface Application to Bulk Solid Water Other Applications Basic Physics I: Electromagnetism Basic Physics II: Quantum Mechanics