In a series of three interlinked papers we present a study of an interplanetary magnetic cloud and its interaction with the Earth's magnetosphere on January 14/15, 1988. This first paper is divided into three parts describing the principal results concerning the magnetic cloud. First, by applying the cylindrically symmetric, magnetic flux rope model to the high time resolution magnetic field and plasma data obtained by the IMP‐8 spacecraft, we show that the axis of the magnetic cloud in question is approximately in the ecliptic and orthogonal to the Earth‐Sun line. We note the presence of pulsations of ∼5‐hour period in the bulk flow speed which are superimposed on an otherwise monotonically falling bulk speed profile. Second, we apply ideal MHD to model the self‐similar, radial expansion of a magnetic cloud of cylindrical geometry. As initial condition for the magnetic field we choose a constant‐α, force‐free magnetic configuration. We demonstrate that the theoretical velocity profile for the free expansion of a magnetic cloud is consistent with observations made during the January 14/15, 1988, magnetic cloud encounter. Comparing model with data, we infer that prior to the start of observations at 1 AU the magnetic cloud had been expanding for 65.4 hours; the radius of the magnetic cloud at the time it arrived at Earth was 0.18 AU; and its expansion speed at 1 AU was ∼114 km/s. Third, we discuss energetic (∼1 MeV) ion data, also from instrumentation on IMP‐8. We highlight the appearance of a sharp enhancement in the intensity of ∼0.5‐MeV ions while IMP‐8 was inside the cloud. These ions travel as a collimated, field‐aligned beam from the west of the Sun. This is an “impulsive” solar event in which particles accelerated at a magnetically well‐connected solar flare arrive promptly at the spacecraft. The observation of solar flare particles inside the cloud suggests that field lines within the magnetic cloud remained connected to the Sun. The observation is, however, inconsistent with the supposition that the cloud is formed of closed magnetic field loops disconnected from the Sun.