MechanicsDevoted to the foundation of mechanics, namely classical Newtonian mechanics, the subject is based mainly on Galileo's principle of relativity and Hamilton's principle of least action. The exposition is simple and leads to the most complete direct means of solving problems in mechanics. The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D Landau has been inserted. 
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One of the most significant moments in my Physics education came during my sophomore year in college. I decided to pick up a copy of "Mechanics" by Landau and Lifshitz that was on reserve in the library for the mechanics class that I was taking. This is the first volume in the internationally renowned series of textbooks on theoretical Physics, the series that has a reputation for its sparse and difficult writing style, as well as the undoubted difficulty and brilliance of the material presented. This is probably the reason why until that point I didn't even bother looking at these books, but for whatever reason that fateful night I decided to take a look at this particular volume. To my surprise, the book was actually pretty readable and the first few chapters revealed an entirely new way of looking at Physics. Until that point I was used to thinking about Physics as a set of laws and equations, relatively succinct but otherwise somewhat arbitrary and adhoc. Landau and Lifshitz's book started from a very different point; it gave some deep underlying principles as a starting point behind the development of physical laws and equations. Based on that I had a new and deeper appreciation of my chosen field of study, and I gained a whole new way of looking at the physical reality.
Granted, the book is really not a walk in the park. Many later chapters can be rather technically demanding, and a prior course on theoretical mechanics at college level is probably the minimal level of preparation that can get a reader through the whole text. There aren't all that many examples that are thoroughly worked out, but all of the problems are given (rather concise) solutions  you still need to fill in some of the more important steps on your own. Mechanics is not an area of active modern research, so this is not necessarily a book that will help one with their scientific careers. However, it provides a solid grounding in some of the most basic physical concepts, and the skills and techniques acquired here can be very important in other areas of Physics. All said, this is a classic textbook that anyone who is serious about a career in Physics would be well advised to go through.
Contents
THE EQUATIONS OF MOTION  1 
2 The principle of least action  2 
3 Galileos relativity principle  4 
4 The Lagrangian for a free particle  6 
5 The Lagrangian for a system of particles  8 
CONSERVATION LAWS  13 
7 Momentum  15 
8 Centre of mass  16 
28 Anharmonic oscillations  84 
29 Resonance in nonlinear oscillations  87 
30 Motion in a rapidly oscillating field  93 
MOTION OF A RIGID BODY  96 
32 The inertia tensor  98 
33 Angular momentum of a rigid body  105 
34 The equations of motion of a rigid body  107 
35 Eulerian angles  110 
9 Angular momentum  18 
10 Mechanical similarity  22 
INTEGRATION OF THE EQUATIONS OF MOTION  25 
12 Determination of the potential energy from the period of oscillation  27 
13 The reduced mass  29 
14 Motion in a central field  30 
15 Keplers problem  35 
COLLISIONS BETWEEN PARTICLES  41 
17 Elastic Collisions  44 
18 Scattering  48 
19 Rutherfords formula  53 
20 Smallangle scattering  55 
SMALL OSCILLATIONS  58 
22 Forced oscillations  61 
23 Oscillations of systems with more than one degree of freedom  65 
24 Vibrations of molecules  70 
25 Damped oscillations  74 
26 Forced oscillations under friction  77 
27 Parametric resonance  80 
36 Eulers equations  114 
37 The asymmetrical top  116 
38 Rigid bodies in contact  122 
39 Motion in a noninertial frame of reference  126 
THE CANONICAL EQUATIONS  131 
41 The Routhian  133 
42 Poisson brackets  135 
43 The action as a function of the coordinates  138 
44 Maupertuis principle  140 
45 Canonical transformations  143 
46 Liouvilles theorem  146 
47 The HamiltonJacob equation  147 
48 Separation of the variable  149 
49 Adiabatic invariants  154 
50 Canonical variables  157 
51 Accuracy of conservation of the adiabatic invariant  159 
52 Conditionally periodic motion  162 
168  