I was given this S&W .38 by my father who got it from his father... The SN is 205xxx and says 38 S&W Special CTG and would appreciate all the info you could provide.
It is a .38 Military & Police Model of 1905, 3rd Change. This model was made from 1909 to 1915, and your gun falls in the middle of the serial number range, so it was probably made around 1912-1913.
Two warnings that have been made before:
1) Keep any ammo labeled +P far, far away
from this gun! It is not safe to fire this modern high-pressure ammo in an old gun without a heat-treated cylinder. It would be a tragedy to blow the cylinder of this family heirloom to bits.
2) This gun predates the S&W hammer block safety. It may discharge if it's dropped on the hammer hard enough to shear off the hammer pivot pin. Do not carry this gun with a live round under the hammer.