The hydrogrossular (HG) mineral series (Ca3Al2(SiO4)(3-x)(OH)(4x); 0x3) are water-bearing minerals found in the upper part of the Earth's mantle and as well as on its surface. They are vital to the planet's hydrosphere under different hydrothermal conditions. The composition and structure of this mineral series are important in geoscience and share many commonalities with cement and clay materials. Other than the end-members of the series grossular (x=0) and katoite (x=3) which have a cubic garnet structure, the structures of the intermediate-members are totally unknown. We used large-scale ab initio modeling to investigate the structures and properties for HG series for x=0, 0.5, 1, 1.5, 2, 2.5, 3. Results indicate that for x>0 and x<3, the structures are tetragonal or nearly tetragonal, which partially justify that this garnet family is known to be cubic or pseudocubic. We also show that there are structural changes related to the disorder introduced with the composition mixing of SiO4 tetrahedra and AlO6 octahedra in the series. Based on the models constructed, the mechanical and interband optical properties of the HG series are calculated. For grossular and katoite, results are in good agreement with the available experimental data. The calculated electronic structure, total bond order explains the atomistic origin of the change in the compressibility of the series. Careful analysis of patterns of these results indicates that the series can be roughly divided into three regions: region I (x=0-0.75), region II (x=0.75-2.25), and region III (x=2.25-3) with high, intermediate, and low Si/H ratio respectively. We also point out the inappropriateness of using the ill-defined concept of treating O4H4 as a compressible structural unit in interpreting the structure and properties of HG series. Furthermore, the phonon spectra of grossular and katoite are calculated.