This is the first volume in a comprehensive two-volume set, 'Advances in Quantum Science', whose second volume is 'Advances in Quantum Science II: Computational and Experimental Approaches'. This volume presents novel quantum theories and computational techniques designed to advance cutting-edge research. It commences with an introduction to updated theories of the quantum electrodynamics and density matrix. Electrons and positrons are examined from diverse theoretical perspectives. Quantum entanglement is explained from the basics to quantum scattering. In Part II, newly developed computational methods are explored. Ultrafast multistage charge transfer in molecular systems is examined with considerations of complex relaxation dynamics. The text delves into computational strategies for managing exciton storage in quantum batteries.  The integration of relativistic effects into the coupled cluster method is introduced. This book aims to assist researchers engaged with electron studies in discovering insights to initiate pioneering research.

Taku Onishi is a Japanese quantum scientist. He graduated from Faculty of Science, Osaka University, Japan in 1998, and gained his Ph.D. from Department of Chemistry, Osaka University, Japan in 2003. He got a permanent position at Faculty of Engineering, Mie University, Japan in 2003. He has been a guest researcher for Department of Chemistry, University of Oslo, Norway since 2010. He was entitled to a visiting professor at University of the Ryukyus, Japan in 2021.  His research covers a variety of research fields such as quantum chemistry, quantum physics, material science and applied mathematics. He has experiences of publishing four Springer books: (1) Quantum Computational Chemistry- Modelling and Calculation for Functional Materials (Monograph, 2018), (2) Theoretical Chemistry for Advanced Nanomaterials- Functional Analysis by Computation and Experiment (Editor, 2020), (3) Ferroelectric Perovskites for High-Speed Memory-A Mechanism Revealed by Quantum Bonding Motion (Monograph,2022), (4) Quantum Science-The Frontier of Physics and Chemistry (Editor,2022).  He is a chair of Quantum Science symposium in renowned ICCMSE conference.