The paper presents a 2+1 dimensional black hole solution in Einstein-Maxwell theory with a negative cosmological constant. This solution is similar to its 3+1 dimensional counterpart, characterized by mass, angular momentum, and charge. Anti-de Sitter space appears as a negative energy state separated from the black hole spectrum by a mass gap. The entropy of the black hole is equal to twice the perimeter length of the horizon. The black hole solution is derived from the action in 2+1 dimensions, which includes a cosmological constant term. The solution is given by a metric that depends on mass M, angular momentum J, and the radius l related to the cosmological constant. The horizon radius is determined by solving the equation N²(r) = 0, with conditions on M and J for the horizon to exist. The vacuum state is obtained by letting the horizon size go to zero, resulting in a metric that describes flat space. Anti-de Sitter space emerges as a "bound state" separated from the black hole spectrum by a mass gap. The black hole has thermodynamic properties similar to its 3+1 dimensional counterpart, with entropy given by twice the horizon perimeter. The Euclidean action is evaluated to determine the free energy and temperature of the black hole. The temperature is found to be related to the horizon radius and the mass. The solution is extended to include electromagnetic fields, with the addition of terms for electromagnetic energy and momentum densities, and a Gauss law constraint. The geometry of the black hole is discussed, with the spacetime having constant negative curvature. The black hole geometry is related to anti-de Sitter space through identifications of points in anti-de Sitter space. The paper concludes that the 2+1 black hole has a rich structure despite the simple nature of gravity in three dimensions. The study of this black hole may provide insights into black hole physics, especially at the quantum level.The paper presents a 2+1 dimensional black hole solution in Einstein-Maxwell theory with a negative cosmological constant. This solution is similar to its 3+1 dimensional counterpart, characterized by mass, angular momentum, and charge. Anti-de Sitter space appears as a negative energy state separated from the black hole spectrum by a mass gap. The entropy of the black hole is equal to twice the perimeter length of the horizon. The black hole solution is derived from the action in 2+1 dimensions, which includes a cosmological constant term. The solution is given by a metric that depends on mass M, angular momentum J, and the radius l related to the cosmological constant. The horizon radius is determined by solving the equation N²(r) = 0, with conditions on M and J for the horizon to exist. The vacuum state is obtained by letting the horizon size go to zero, resulting in a metric that describes flat space. Anti-de Sitter space emerges as a "bound state" separated from the black hole spectrum by a mass gap. The black hole has thermodynamic properties similar to its 3+1 dimensional counterpart, with entropy given by twice the horizon perimeter. The Euclidean action is evaluated to determine the free energy and temperature of the black hole. The temperature is found to be related to the horizon radius and the mass. The solution is extended to include electromagnetic fields, with the addition of terms for electromagnetic energy and momentum densities, and a Gauss law constraint. The geometry of the black hole is discussed, with the spacetime having constant negative curvature. The black hole geometry is related to anti-de Sitter space through identifications of points in anti-de Sitter space. The paper concludes that the 2+1 black hole has a rich structure despite the simple nature of gravity in three dimensions. The study of this black hole may provide insights into black hole physics, especially at the quantum level.