The potential energy curves (PECs) of all covalent states of Molecular Astatine (At2) have been investigated in this work within a four-component relativistic framework using the MOLFDIR program package. The ground state was determined using multireference configuration interaction with all single and double excitations including Davidson size-extensivity correction (MRCISD+Q) whereas the 22 excited states were treated by complete open shell configuration interaction (COSCI). Spectroscopic constants (Re,ωe,ωexe,ωeye, De,Be,αe,βe,Te) are presented for all states as well as vertical excitations obtained at COSCI, MRCISD and MRCISD+Q levels. In addition, it is also presented accurate extended Rydberg analytical form for the ground state X: (1)0g+.