  Our studies evidence an anisotropic magnetic order below $T_N = 32$~K.
Susceptibility data in small fields of about 1~T reveal an antiferromagnetic
(AFM) order for $H \perp c$, whereas for $H \parallel c$ the data are
reminiscent of a field-induced ferromagnetic (FM) structure. At low
temperatures and for $H \perp c$, the field-dependent magnetization and AC
susceptibility data evidence a metamagnetic transition at $H^+ = 5$~T, which is
absent for $H \parallel c$. We assign this to a transition from a planar
cycloidal spin structure at low fields to a planar fan-like arrangement above
$H^+$. A fully FM polarized state is obtained above the saturation field of
$H_{\perp S} = 23.7$~T at 2~K with a magnetization of $M_s = 2.8$~$\mu_{\rm
B}{\rm /Cr}$. For $H \parallel c$, $M(H)$ monotonously increases and saturates
at the same $M_s$ value at $H_{\parallel S} = 25.1$~T at 4.2~K. Above $T_N $,
the magnetic susceptibility and specific heat indicate signatures of two
dimensional (2D) frustration related to the presence of planar ferromagnetic
and antiferromagnetic exchange interactions. We found a pronounced nearly
isotropic maximum in both properties at about $T^* = 45$~K, which is a clear
fingerprint of short-range correlations and emergent spin fluctuations.
Calculations based on a planar 2D Heisenberg model support our experimental
findings and suggest a predominant FM exchange among nearest and AFM exchange
among third-nearest neighbors. Only a minor contribution might be assigned to
the antisymmetric Dzyaloshinskii-Moriya interaction possible related to the
non-centrosymmetric polar space group $R3m$. Due to these competing
interactions, the magnetism in AgCrSe$_{2}$, in contrast to the oxygen based
delafossites, can be tuned by relatively small, experimentally accessible,
magnetic fields, allowing us to establish the complete anisotropic magnetic
$H-T$ phase diagram in detail.
