In 1927 Einstein sent two brief communications to the Prussian Academy of Sciences on Kaluza's five-dimensional theory. In his Einstein biography, Abraham Pais asserted that he could not understand the reasons that pushed Einstein to communicate his work. Indeed, Einstein's paper seems to be very close to Oskar Klein's approach, published in 1926. The question seems to be yet unanswered, also in recent works. We analysed the differences between Einstein's and Klein's work and we propose a new interpretation of Einstein's approach. In 1927, he tried to use Weyl's scale invariance in order to construct a theory covering macroscopic as well as microscopic phenomena. In constructing a five-dimensional action, Einstein used in a modern way the idea of ``gauge invariance''. Furthermore, we propose an additional motivation for the fact that he did not mention Klein's and Vladimir Fock's contributions in his first communication and we show further evidences which would confirm also Paul Halpern's recent proposal. As a consequence of our interpretation of the role of conformal transformations, we suggest that in 1927 Einstein did not consider the fifth dimension as real and that his approach, unlike Klein's attempt, cannot be considered inconsistent.

In this talk, delivered at the Oscar Klein Centenary Symposium in Stockholm, I review the 1938 conference held in Warsaw devoted to \lq \lq New Theories in Physics". I review all of the talks presented at this meeting and discuss in detail Klein's paper where he proposed a unified model of electromagnetism and the nuclear force that foreshadowed the later developments of non-Abelian gauge theories.

Lecture notes for a 'Part III' course 'Black Holes' given in DAMTP, Cambridge. The course covers some of the developments in Black Hole physics of the 1960s and 1970s.