TEMPO2 is a new pulsar timing package that improves upon previous methods by achieving a precision of 1 ns, a factor of 100 more accurate than earlier techniques. It is compliant with the IAU 1991 and 2000 resolutions, using the International Celestial Reference System, Barycentric Coordinate Time, and up-to-date precession, nutation, and polar motion models. TEMPO2 provides a generic and extensible set of tools for analyzing and visualizing pulsar timing data. It includes a new scheme for predictive use of the timing model, which removes processing artifacts by properly modeling the frequency dependence of pulse phase. The paper describes the timing model, its accuracy, and differences from earlier work. It also outlines the algorithms used in TEMPO2 to achieve 1 ns accuracy, methods to simulate gravitational wave effects, and utilities to set limits on a gravitational wave background. Section 2 discusses real and simulated pulse arrival times used for testing TEMPO2. Section 3 describes the conversion of site arrival times to the pulsar frame using clock correction files, propagation delays, and planetary ephemeris. Section 4 describes the fitting algorithms for single datasets. Section 5 discusses analysis methods for fitted parameters and their uncertainties. Section 6 contains information on TEMPO2 routines for timing residuals. Section 7 describes the predictive facility of TEMPO2. TEMPO2 includes a new free format for measured pulse arrival times, allowing user-definable parameters such as backend systems, observation length, and bandwidth. It can handle TOAs from different observatories with different back-end systems and receivers, which often result in constant offsets or "jumps" between sets of TOAs. TEMPO2 can fit for such jumps between observations at different telescopes. It also allows for the analysis of multiple pulsars simultaneously, which is advantageous for studying double-pulsar systems, searching for gravitational waves, or examining terrestrial time standards. The timing procedure starts by converting measured topocentric TOAs to the pulse emission time in the pulsar frame, ignoring the frequency-independent propagation delay from the pulsar to the SSB. The transformation is described in detail in Paper II. The transformation includes various clock corrections, atmospheric propagation delays, Solar System Einstein and Roemer delays, the dispersive component of light travel time, secular motion effects, and orbital motion terms. Table 2 lists various effects that must be considered when forming barycentric arrival times from observed TOAs. TEMPO2 handles clock corrections by transforming measurements into the Geocentric Celestial Reference System (GCRS), using the International Terrestrial Reference Frame (ITRF). It includes a database of ASCII files tabulating offsets between named pairs of clocks. The scheme allows for the application of corrections based on a manually or automatically determined sequence derived from linear interpolation of values from files in the database. It also allows for the production of TEMPO2 format filesTEMPO2 is a new pulsar timing package that improves upon previous methods by achieving a precision of 1 ns, a factor of 100 more accurate than earlier techniques. It is compliant with the IAU 1991 and 2000 resolutions, using the International Celestial Reference System, Barycentric Coordinate Time, and up-to-date precession, nutation, and polar motion models. TEMPO2 provides a generic and extensible set of tools for analyzing and visualizing pulsar timing data. It includes a new scheme for predictive use of the timing model, which removes processing artifacts by properly modeling the frequency dependence of pulse phase. The paper describes the timing model, its accuracy, and differences from earlier work. It also outlines the algorithms used in TEMPO2 to achieve 1 ns accuracy, methods to simulate gravitational wave effects, and utilities to set limits on a gravitational wave background. Section 2 discusses real and simulated pulse arrival times used for testing TEMPO2. Section 3 describes the conversion of site arrival times to the pulsar frame using clock correction files, propagation delays, and planetary ephemeris. Section 4 describes the fitting algorithms for single datasets. Section 5 discusses analysis methods for fitted parameters and their uncertainties. Section 6 contains information on TEMPO2 routines for timing residuals. Section 7 describes the predictive facility of TEMPO2. TEMPO2 includes a new free format for measured pulse arrival times, allowing user-definable parameters such as backend systems, observation length, and bandwidth. It can handle TOAs from different observatories with different back-end systems and receivers, which often result in constant offsets or "jumps" between sets of TOAs. TEMPO2 can fit for such jumps between observations at different telescopes. It also allows for the analysis of multiple pulsars simultaneously, which is advantageous for studying double-pulsar systems, searching for gravitational waves, or examining terrestrial time standards. The timing procedure starts by converting measured topocentric TOAs to the pulse emission time in the pulsar frame, ignoring the frequency-independent propagation delay from the pulsar to the SSB. The transformation is described in detail in Paper II. The transformation includes various clock corrections, atmospheric propagation delays, Solar System Einstein and Roemer delays, the dispersive component of light travel time, secular motion effects, and orbital motion terms. Table 2 lists various effects that must be considered when forming barycentric arrival times from observed TOAs. TEMPO2 handles clock corrections by transforming measurements into the Geocentric Celestial Reference System (GCRS), using the International Terrestrial Reference Frame (ITRF). It includes a database of ASCII files tabulating offsets between named pairs of clocks. The scheme allows for the application of corrections based on a manually or automatically determined sequence derived from linear interpolation of values from files in the database. It also allows for the production of TEMPO2 format files