The main site of dust formation is believed to be the cool envelopes around AGB stars. Nearly all AGB stars can be identified as long-period variables (LPVs) with large amplitude pulsation. Shock waves produce by the strong pulsation and radiation pressure on newly formed dust grains drive dusty stellar winds with high mass-loss rates. IR observations of AGB stars identify various dust species in different physical conditions. Radio observations of gas phase materials are helpful to understand the overall properties of the stellar winds. In this paper, we review (i) classification of AGB stars; (ii) IR two-color diagrams of AGB stars; (iii) pulsation of AGB stars; (iv) dust around AGB stars including dusty stellar winds; (v) dust envelopes around AGB stars; (vi) mass-loss and evolution of AGB stars; and (vii) contribution of AGB dust to galactic environments. We discuss various observational evidences and their theoretical interpretations.

We have solved the radiative transfer problem using a Sobolev approximation with an escape probability method in case of the supersonic expansion of a stellar envelope to an ambient medium. The radiation from the expanding envelope turns out to produce a P-Cygni type profile. In order to investigate the morphology of the theoretical P-Cygni type profile, we have treated V∞,Vsto,β (parameter for the velocity field), M and є (parameter for collisional effect) as model parametrs. We have found that the velocity field and the mass loss rate affect the shapes of the P-Cygni type profiles most effectively. The secondarily important factors are V∞, Vsto. The collisional effect tends to make the total flux increase but not so .much in magnitude. We have infered some physical parameters of 68 Cyg, HD24912, and ℇ persei such as V∞, M from the model calculation, which shows a good agreement with the observational results.