We report on a detailed study of the optical properties of CsV$_{3}$Sb$_{5}$ at a large number of temperatures above and below the charge-density-wave (CDW) transition. Above the CDW transition, the low-frequency optical conductivity reveals two Drude components with distinct widths. An examination of the band structure allows us to ascribe the narrow Drude to multiple light and Dirac bands, and the broad Drude to the heavy bands near the $M$ points which form saddle points near the Fermi level. Upon entering the CDW state, the opening of the CDW gap is clearly observed. A large portion of the broad Drude is removed by the gap, whereas the narrow Drude is not affected. Meanwhile, an absorption peak associated with interband transitions near the saddle points shifts to higher energy and grows in weight. These observations are consistent with the scenario that the CDW in CsV$_{3}$Sb$_{5}$ is driven by nesting of Fermi surfaces near the saddle points at $M$.
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