Aluminas are materials of high technological importance that show a fascinating structural flexibility, with a large amount of different phases (α, γ, η, δ, κ, χ,...) and phase transitions at relatively high temperatures. This variety provides the different alumina phases with a wide range of properties but at the same time makes experimental and theoretical investigations on them difficult to perform. In particular, a fundamental understanding at the atomistic level is lacking for metastable aluminas, for most of which not even the atomic structure is well known. In the present Thesis, I report on first-principles theoretical investigations at the quantum-mechanical level, based on the density-functional theory (DFT), to study the stability and bonding of the metastable κ-Al2O3. The motivation for this is three-fold. First, the use of κ-Al2O3 as a wear-resistant coating on cemented-carbide cutting tools, deposited with chemical-vapor deposition (CVD), provides a high technological interest for this material. Second, basic understanding of the stability of a metastable alumina yields general insights into metastable-alumina properties. Third, the study of a relatively complex ionic crystal like κ-Al2O3 can be used to investigate the general problem of ion-crystal stability. The work is performed in three parts: (i) The atomic and electronic bulk structures of κ-Al2O3 are determined; (ii) The structure and stability of the (001) and (001¯) surfaces are understood; (iii) The thermodynamics of the Al2O3 nucleation on TiC(111) is investigated. The results yield fundamental knowledge on the CVD growth process of κ-Al2O3, on the stability of metastable aluminas, and on the cohesion of low-symmetry ionic crystals in general. The limited validity of point-charge models for ion-crystal stability is discussed. A surprising prediction of a 1D electron gas at the κ-Al2O3(001¯) surface is furthermore revealed.