Mononuclear copper complexes (Hdapt)[Cu(Hpydc)(pydc)(H2O)]•H2O (1) and (H2aba)[Cu(pydc)2(Haba)]2•9H2O (2) {where dapt = 2,4-diamino-6-phenyl-1,3,5-triazine, aba = 3-aminobenzylamine, and H2pydc = 2,3-pyridinedicarboxylic acid} were synthesized and fully characterized. Among them, compound 1 is a very good building block for the bottom up synthesis of a dicopper(II) derivative (Hdapt)4[Cu2(pydc)4]•10H2O (3), a heterometallic 2D coordination polymer {[Zn(H2O)4Cu(pydc)2]•3H2O)}n (4), and a 3D metal-organic framework {[Gd(H2O)5Cu1.5(pydc)3] •5H2O}n (5). The structures of 1–3 reveal the formation of distinct 2D (in 1, 3) and 3D (in 2) H-bonded networks driven by strong hydrogen bonds between the Cu(pydc)2-containing anions and amine cations. The underlying H-bonded (in 1–3) and metal-organic (in 4, 5) networks were classified from the topological viewpoint, disclosing the following topologies: a SP 1-periodic net (4,4)(0,2) in 1, a topologically unique net in 2, a 3,6L17 layer in 3, a 3,4L13 layer in 4, and an alb-3,6-P42/mnm framework in 5. Thermal properties of 1–5 as well as the decomposition of 4 and 5 toward the synthesis of nano-dimensional mixed metal oxides were investigated.