the (English translation) of the lecture of David Hilbert at the International Congress of Mathematicians at Paris in 1900 (with the list of “Hilbert’s problems”) is here
Felix E. Browder. Mathematical Developments Arising from Hilbert Problems. Proceedings of Symposia in Pure Mathematics. XXVIII.2. American Mathematical Society.
Lectures by Hilbert on physics and especially on general relativity are collected here:
Hilbert's theorem 90