Lev Davidovich Landau was born on January 22, 1908 in Baku, U.S.S.R (now Azerbaijan). A brilliant student, he had finished secondary school by the age of 13. He enrolled in the University of Baku a year later, in 1922, and later transferred to the University of Leningrad, from which he graduated with a degree in physics. Landau did graduate work in physics at Leningrad's Physiotechnical Institute, at Cambridge University in England, and at the Institute of Theoretical Physics in Denmark, where he met physicist Neils Bohr, whose work he greatly admired. Landau worked in the Soviet Union's nuclear weapons program during World War II, and then began a teaching career. Considered to be the founder of a whole school of Soviet theoretical physicists, Landau was honored with numerous awards, including the Lenin Prize, the Max Planck Medal, the Fritz London Prize, and, most notably, the 1962 Nobel Prize for Physics, which honored his pioneering work in the field of low-temperature physics and condensed matter, particularly liquid helium. Unfortunately, Landau's wife and son had to accept the Nobel Prize for him; Landau had been seriously injured in a car crash several months earlier and never completely recovered. He was unable to work again, and spent the remainder of his years, until his death in 1968, battling health problems resulting from the accident. Landau's most notable written work is his Course of Theoretical Physics, an eight-volume set of texts covering the complete range of theoretical physics. Like several other of Landau's books, it was written with Evgeny Lifshitz, a favorite student, because Landau himself strongly disliked writing. Some other works include What is Relativity?, Theory of Elasticity, and Physics for Everyone.
Goldstein, surely. L&L is great, but it is not self-contained and the exposition isn't that great (there's certainly a lot lost in translation). Actually, if you don't already have mastery over basic Lagrangian and Hamiltonian physics (for example, if you cannot derive the Euler-Lagrange equations from the principle of least action, or if you cannot perform a Legendre transformation on a given Hamiltonian), I recommend The Theoretical Minimum: What You Need to Know to Start Doing Physics. The first half of the book will be way too basic for someone who already knows Maxwell's equations, but the second half is perfect. Goldstein and L&L both overcomplicate things. Once you're confident with Hamiltonians, you can move straight to quantum mechanics, no need to dally on Goldstein.
Also, neither is a good introduction to special relativity - it's pretty much assumed you know it at an undergraduate level (why the "barn and pole paradox" and "twin paradox" are not paradoxes, how to do a Lorentz transformation, etc.). So you might want to supplement yourself with a quick perusal of Special Relativity (M.I.T. Introductory Physics Series), which is a first or second year undergraduate introduction to special relativity. Likewise the Feynman lectures recommended in the comments are first or second year undergraduate introductions to subjects, and maybe are not what you're looking for. Goldstein (chapter 7 if I recall correctly) then allows you to derive lots of great more difficult consequences of special relativity.
If you have exposure to Maxwell's equations, going to field theory won't be much of a problem, as you simply substitute "Lagrangian" for "Lagrangian density". Goldstein also covers this, and L&L's second book "Classical Field Theory" is great here, too. But again L&L isn't self-contained and the exposition can be confusing.
tl;dr: Goldstein's book and both books by L&L are all worth having on your shelf. Both are at the introductory graduate physics level, and try to be self contained but practically rely on some exposure to hamiltonians and lagrangians, and mastery over special relativity. You do NOT need to touch (let alone master) these books to move on to nonrelativistic quantum mechanics.