This paper investigates the cosmological implications of $ f(Q) $ gravity in non-flat universes. $ f(Q) $ gravity is a modified theory of gravity based on non-metricity, and it has second-order field equations, making it attractive for cosmological applications. The study focuses on the cosmological behavior of $ f(Q) $ gravity in non-flat geometry, where the universe is not spatially flat. The authors perform a detailed dynamical-system analysis, keeping the $ f(Q) $ function completely arbitrary. They find that the cosmological scenario admits a dark-matter dominated point and a dark-energy dominated de Sitter solution which can attract the universe at late times. However, the main result is that there are additional critical points which exist solely due to curvature. These include curvature-dominated accelerating points which are unstable and can describe the inflationary epoch, as well as a point where dark-matter and dark-energy density parameters are both between zero and one, alleviating the coincidence problem. There is also a saddle point dominated by curvature. The authors apply their general analysis to the power-law case $ f(Q) = \eta Q^n $, showing that the universe can exhibit a thermal history with a peak in curvature density parameter at intermediate times. These features, along with possible indications that non-zero curvature could alleviate cosmological tensions, make $ f(Q) $ gravity in non-flat geometry an interesting and promising approach. The study highlights the unique features of $ f(Q) $ gravity in non-flat universes, including the possibility of a saddle matter-dominated era and a stable late-time dark-energy era. The results suggest that $ f(Q) $ gravity in non-flat geometry can provide a viable alternative to other modified gravity theories.This paper investigates the cosmological implications of $ f(Q) $ gravity in non-flat universes. $ f(Q) $ gravity is a modified theory of gravity based on non-metricity, and it has second-order field equations, making it attractive for cosmological applications. The study focuses on the cosmological behavior of $ f(Q) $ gravity in non-flat geometry, where the universe is not spatially flat. The authors perform a detailed dynamical-system analysis, keeping the $ f(Q) $ function completely arbitrary. They find that the cosmological scenario admits a dark-matter dominated point and a dark-energy dominated de Sitter solution which can attract the universe at late times. However, the main result is that there are additional critical points which exist solely due to curvature. These include curvature-dominated accelerating points which are unstable and can describe the inflationary epoch, as well as a point where dark-matter and dark-energy density parameters are both between zero and one, alleviating the coincidence problem. There is also a saddle point dominated by curvature. The authors apply their general analysis to the power-law case $ f(Q) = \eta Q^n $, showing that the universe can exhibit a thermal history with a peak in curvature density parameter at intermediate times. These features, along with possible indications that non-zero curvature could alleviate cosmological tensions, make $ f(Q) $ gravity in non-flat geometry an interesting and promising approach. The study highlights the unique features of $ f(Q) $ gravity in non-flat universes, including the possibility of a saddle matter-dominated era and a stable late-time dark-energy era. The results suggest that $ f(Q) $ gravity in non-flat geometry can provide a viable alternative to other modified gravity theories.