The paper addresses the multiple forms of representation that human gesture takes at different levels for human computer interaction, ranging from gesture acquisition to mathematical model for analysis, pattern for recognition, record for database up to end-level application event triggers. A mathematical model for gesture as command is presented. We equally identify and provide particular models for four different types of gestures by considering both posture information and underlying motion trajectories. The problem of constructing gesture dictionaries is further addressed by taking into account similarity measures and dictionary discriminative features.