Pulsars – rapidly rotating highly magnetised neutron stars – have many applications in physics and astronomy. Striking examples include the confirmation of the existence of gravitational radiation [359, 360, 371], the first extra-solar planetary system [403, 298] and the first detection of gas in a globular cluster . The diverse zoo of radio pulsars currently known is summarized in Figure 1.
Pulsar research has proceeded at a rapid pace during the first three versions of this article [221, 222, 224]. Surveys with the Parkes radio telescope , at Green Bank , Arecibo  and the Giant Metre Wave Radio Telescope  have more than doubled the number of pulsars known a decade ago. With new instrumentation coming online, and new telescopes planned [111, 368, 374], these are exciting times for pulsar astronomy.
The aims of this review are to introduce the reader to the field and to focus on some of the many applications of pulsar research in relativistic astrophysics. We begin in Section 2 with an overview of the pulsar phenomenon, a review of the key observed population properties, the origin and evolution of pulsars and the main search strategies. In Section 3, we review present understanding in pulsar demography, discussing selection effects and their correction techniques. This leads to empirical estimates of the total number of normal and millisecond pulsars (see Section 3.3) and relativistic binaries (see Section 3.4) in the Galaxy and has implications for the detection of gravitational radiation by current and planned telescopes. Our review of pulsar timing in Section 4 covers the basic techniques (see Section 4.2), timing stability (see Section 4.3), binary pulsars (see Section 4.4), and using pulsars as sensitive detectors of long-period gravitational waves (see Section 4.7). We conclude with a brief outlook to the future in Section 5. Up-to-date tables of parameters of binary and millisecond pulsars are included in Appendix A.
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