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In this paper, we study normalized solutions to theChern-Simons-Schr\"odinger system, which is a gauge-covariant nonlinearSch\"oridnger system with a long-range electromagnetic field, arising innonrelativistic quantum mechanics theory. The solutions correspond to criticalpoints of the underlying energy functional subject to the $L^2$-normconstraint. Our research covers several aspects. Firstly, in the masssubcritical case, we establish the compactness of any minimizing sequence tothe associated global minimization problem. As a by-product of the compactnessof any minimizing sequence, the orbital stability of the set of minimizers tothe problem is achieved. In addition, we discuss the radial symmetry anduniqueness of minimizer to the problem. Secondly, in the mass critical case, weinvestigate the existence and nonexistence of normalized solution. Finally, inthe mass supercritical case, we prove the existence of ground state andinfinitely many radially symmetric solutions. Moreover, the instability ofground states is explored

Normalized solutions to the Chern-Simons-Schr\"odinger system