Imagine two twin brothers, such that one of them goes on a long round trip in space, at high speed, while the other stays home. Special Relativity claims that, when the traveling twin reunites with his brother, he will be younger than the latter. Although informally referred to as a "paradox", this fact can be logically deduced from the principles of the theory and its "paradoxical" aspect is easily disposed of if one realizes that the traveling twin necessarily underwent acceleration while the sedentary twin did not.
Although the effect is quite small if the travel velocity is much smaller than the speed of light, is has been verified in precision measurements with clocks carried by airplanes.
Here is the link to the text “Concepts of Special Relativity” in PDF format. The twin paradox is analyzed in Chapter 8. As mentioned above, the approach known as k-calculus is adopted, so that the result is first derived in terms of Bondi's k factor. The more familiar expression, in terms of the so-called Lorentz factor is then deduced, by using results obtained in Chapter 4 to express the k factor in terms of the relative velocity.
A numerical example of the twin paradox can be found in Appendix A.6.
In order to understand clearly the concepts and the nomenclature used, it is recommended to begin by reading the first three chapters of the text.
An animation software written in the Java language is available. The twin paradox is illustrated by the seventh (and last) animation proposed.
If you are interested in a particular topic of Special Relativity, here is a list of the topics covered in the text and in the software. Clicking on an item in this list, will open a page which briefly introduces that topic and indicates the parts of the text and of the software in which it is treated.