This article documents the performance of the ATLAS muon identification and reconstruction using the LHC dataset recorded at $\sqrt{s} = 13$ TeV in 2015. Using a large sample of $J/\psi \rightarrow \mu \mu $ and $Z\rightarrow \mu \mu $ decays from 3.2 fb$^{-1}$ of pp collision data, measurements of the reconstruction efficiency, as well as of the momentum scale and resolution, are presented and compared to Monte Carlo simulations. The reconstruction efficiency is measured to be close to $99~\%$ over most of the covered phase space ( $|\eta |<2.5$ and $5 < p_{\mathrm {T}} < 100$ GeV). The isolation efficiency varies between 93 and $100~\%$ depending on the selection applied and on the momentum of the muon. Both efficiencies are well reproduced in simulation. In the central region of the detector, the momentum resolution is measured to be $1.7~\%$ ( $2.3~\%$ ) for muons from $J/\psi \rightarrow \mu \mu $ ( $Z\rightarrow \mu \mu $ ) decays, and the momentum scale is known with an uncertainty of $0.05~\%$ . In the region $|\eta |>2.2$ , the $p_{\mathrm {T}} $ resolution for muons from $Z\rightarrow \mu \mu $ decays is $2.9~\%$ while the precision of the momentum scale for low- $p_{\mathrm {T}} $ muons from $J/\psi \rightarrow \mu \mu $ decays is about $0.2~\%$
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