The wordy title of this map is "Map showing the line of the Alabama & Tennessee River Rail Road and its proposed extensions; exhibiting also the contiguous mineral deposits and zone of production". The dark blue line indicates the existing railroad; the dark green lines are proposed extensions.
The company had incorporated in March 1848 under an act of the Alabama legislature. By 1862 about 135 miles of the line ran from Selma to Blue Mountain and toward Dalton, Georgia. By February 1867, after acts of both the Alabama and Georgia legislatures, the line was merged with one in Georgia to become the Selma, Rome and Dalton Railroad. By 1894 the road had become part of the Southern Railroad Company.
Digital versions of this map in various sizes/formats can be found at the Library of Congress web site.
A very good history is Wayne Cline's book Alabama Railroads.