This volume consists of four parts. The first part is a biographical sketch of the life and work of Professor Sir Rudolf Peierls, eminent mathematical physicist. The second part consists of the symposium lectures on a broad range of research areas covering topics like dendritic growth, solar neutrinos, supernovae and heavy ions, quantum tunneling, astrophysics, nuclear weapons, string theory and theoretical physics. The third part provides an account of the life and scientific achievements of Professor Tony Hilton Royle Skyrme, a close associate of Professor Peierls. The last part contains reminiscences and birthday greetings to Sir Peierls.