Traditional presentations of relativity theory start with the introduction of Lorentz-transformations from which the peculiar phenomena of the theory ─ time dilatation, Lorentz-contraction, the velocity addition formula, etc. ─ follow. Though this is certainly the most logical approach, it seems rather unfortunate from a pedagogical point of view since a convincing and conceptually transparent explanation of the Lorentz-transformation itself presents a task of considerable difficulty. Lorentz-transformation is based on both the constancy of the velocity of light and Einstein-synchronization prescription, and the interrelation between these two constituents is open to the frequent misunderstanding that the constancy of the light velocity is enforced by the special synchronization of clocks rather than being the law of nature. In order to avoid this pitfall an ad hoc though rigorous presentation of the theory's observational peculiarities in Part 1 precedes the introduction of the Lorentz-transformation (and any synchronization procedure). After the introduction of these transformations in Part 2 those same relativistic effects are reconsidered this time in a systematic manner. Part 3 is devoted to the fundamentals of general relativity.
Part 1. From time dilatation to E = mc2
Reference frames and coordinate systems
The optical Doppler-effect and time dilatation
Relativity of simultaneity
The proper time and the twin paradox
The velocity addition formula
Equation of motion of a point mass
Does the mass increase with the velocity?
The kinetic energy of a point mass
Rest energy: The E = mc2 law
Are mass and energy equivalent to each other?
Part 2. The Lorentz-transformation
One way measurement of the speed of light
Classification of space-time intervals
The causality paradox
Interrelation of proper time and coordinate time in inertial frames
Calculation of the twin paradox
Coordinates in accelerating reference frames: Twin paradox as seen from the
Coordinates in accelerating reference frames: The rotating Earth
Does the perimeter of a rotating disk become contracted?
Do moving bodies seem shorter?
Addition of velocities reconsidered
Equation of motion of a point mass reconsidered
The momentum four-vector
Zero mass particles
Transformation of the electromagnetic field
Part 3. Fundamentals of general relativity
Inertial and gravitational mass
The principle of equivalence
The precise meaning of the relation m* = m
Locality of the inertial frames
The GP-B experiment
Gravitational red shift.