  Three types of reciprocity laws for arithmetic surfaces are established. For
these around a point or along a vertical curve, we first construct $K_2$ type
central extensions, then introduce reciprocity symbols, and finally prove the
law as an application of Parshin-Beilinson's theory of adelic complex. For
reciprocity law along a horizontal curve, we first introduce a new type of
arithmetic central extensions, then apply our arithmetic adelic cohomology
theory and arithmetic intersection theory to prove the related reciprocity law.
  All this can be interpreted within the framework of arithmetic central
extensions. We add an appendix to deal with some basic structures of such
extensions.
