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it really depends on the level you want to achieve. also, "chemistry" is a general term and many branches of chemistry are pretty different for each other.
zumdahl, as the other anon suggested, is a good start. allow me to suggest other excellent textbooks which approach other branches of chemistry.
analytical chemistry: douglas skoog, gary d. christian
organic: david r. klein, jonathan clayden
inorganic and general: catherine e. housecroft; chemistry, the central science
nmr spectroscopy: harald gunther
physical chemistry: atkins
thermodynamical phenomena in chemistry: herbert callen
electrochemistry: bard faulkner
quantum chemistry and orbital interactions: fleming i, thomas a. albright and lucjan piela
the math prerequisites depend on the field of study.
organic and inorganic don't use fancy maths
analytical requires a bit of statistics and knowing how to use derivatives
the whole branch of physical chemistry requires profound knowledge of calculus.
delving into more complicated fields like ligand field theory, orbitals and everything related to quantum chemistry requires that you know how to use hamiltonians and schrodingers equation.
i've explained everything briefly, because it would take too much time to "dissect" the prerequisites of every single branch i've mentioned earlier
