  This paper reports the photospheric, magnetic and circumstellar gas
characteristics of the magnetic B8p star 36 Lyncis (HD 79158). Using archival
data and new polarised and unpolarised high-resolution spectra, we redetermine
the basic physical properties, the rotational period and the geometry of the
magnetic field, and the photospheric abundances of various elements.}{Based on
magnetic and spectroscopic measurements, we infer an improved rotational period
of $3.83475\pm 0.00002$ d. We determine a current epoch of the longitudinal
magnetic field positive extremum (HJD 2452246.033), and provide constraints on
the geometry of the dipole magnetic field ($i\geq 56\degr$, $3210 {\rm G}\leq
B_{\rm d}\leq 3930$ G, $\beta$ unconstrained). We redetermine the effective
temperature and surface gravity using the optical and UV energy distributions,
optical photometry and Balmer line profiles ($T_{\rm eff}=13300\pm 300$ K,
$\log g=3.7-4.2$), and based on the Hipparcos parallax we redetermine the
luminosity, mass, radius and true rotational speed ($L=2.54\pm 0.16 L_\odot,
M=4.0\pm 0.2 M_\odot, R=3.4\pm 0.7 R_\odot, v_{\rm eq}=45-61.5$ \kms). We
measure photospheric abundances for 21 elements using optical and UV spectra,
and constrain the presence of vertical stratification of these elements. We
perform preliminary Doppler Imaging of the surface distribution of Fe, finding
that Fe is distributed in a patchy belt near the rotational equator. Most
remarkably, we confirm strong variations of the H$\alpha$ line core which we
interpret as due to occultations of the star by magnetically-confined
circumstellar gas.
