Nonlinear transport phenomena offer powerful insights into symmetry, topology, and quantum geometry in quantum materials. Second-order responses, such as the nonlinear Hall effect and second harmonic generation –– arise from Berry curvature dipoles and quantum metric effects, and are highly sensitive to the underlying symmetries of the system. In particular, conventional Weyl semimetals, where inversion symmetry is broken, host tilted Weyl cones that yield asymmetric Berry curvature distributions and large Berry curvature dipoles that enable nonlinear anomalous Hall conductivity even in time-reversal symmetric systems and without external magnetic fields. Further breaking of time-reversal symmetry can activate additional nonlinear responses by the quantum metric dipole. Theoretical and experimental studies have demonstrated that the presence of Weyl nodes and the resulting topological Berry curvature structure underpin a robust class of nonlinear responses in such materials. Building on this understanding, we propose to extend the study of nonlinear transport to a new class of materials, called altermagnets, which combine antiferromagnetic order with PT symmetry breaking and momentum-space spin splitting, despite having no net magnetization. In particular, Weyl altermagnets recently proposed in compounds such as CrSb and Ca₃Ru₂O₇ present a unique opportunity to explore nonlinear transport phenomena that emerge from the coexistence of symmetry-protected Weyl nodes and collinear magnetic order. Although the total Berry curvature in many altermagnets cancels due to symmetry, system-dependent symmetry breaking can lead to finite Berry curvature in specific momentum-space regions, allowing not only for the possibility of anomalous Hall effects but also enabling nonlinear Hall effects through a finite Berry curvature dipole. More generally, the nonlinear Hall effect can emerge even when the total Berry curvature is zero, as it is governed by the Berry curvature dipole –– the first moment of the Berry curvature distribution. Weyl altermagnet (Ca₃Ru₂O₇) revealed that nonlinear transport, especially from quantum metric dipole effects, can act as a sensitive probe of hidden magnetic, phase transitions, and structural orders –– offering a powerful tool beyond the reach of standard crystallography or spectroscopy. The nonlinear transport properties of altermagnets remain largely unexplored, positioning this field at the forefront of condensed matter research and offering new opportunities to uncover subtle symmetry-breaking mechanisms. This project proposes a comprehensive first-principles and model Hamiltonian-based investigation into nonlinear charge and spin transport in Weyl altermagnetic materials. We aim to discover new altermagnets and understand how PT and hidden symmetry breaking, Weyl topology, and quantum geometry collectively generate nonlinear Hall conductivity, shift currents, and optically induced spin responses in systems with weak spin-orbit coupling. Through density functional theory and symmetry-based modeling, we will map the Berry curvature dipole and quantum metric, quantify geometric contributions to transport, and study how these nonlinearities can be tuned via external perturbations such as strain, electric fields, or light. By bridging condensed matter theory, materials modeling, and quantum topology, the outcomes will contribute to both foundational physics and emerging technologies in next-generation THz spintronics to realize ultrafast, low-power, and energy-efficient devices.