  Using the PMAS Integral Field Unit on the Calar Alto 3.5m telescope we
observed the southern component (Markarian 59) of the `cometary' starburst
galaxy NGC 4861. Mrk 59 is centred on a giant nebula and concentration of stars
1 kpc in diameter. Strong $\rm H\alpha$ emission points to a star-formation
rate (SFR) at least 0.47 $\rm M_{\odot}yr^{-1}$. Mrk 59 has a very high
[OIII]$\rm\lambda5007/H\beta$ ratio, reaching 7.35 in the central nebula, with
a second peak at a star-forming hotspot further north. Fast outflows are not
detected but nebular motion and galaxy rotation produce relative velocities up
to 40 km $\rm s^{-1}$. Spectral analysis of different regions with `Fitting
Analysis using Differential evolution Optimisation' (FADO) finds that the stars
in the central and `spur' nebulae are very young, $\rm \leq125~Myr$ with a
large $\rm <10~Myr$ contribution. Older stars ($\rm \sim 1~Gyr$) make up the
northern disk component, while the other regions show mixtures of 1 Gyr age
with very young stars. This and the high specific SFR $\rm\sim 3.5~Gyr^{-1}$
imply a bimodal star formation history, with Mrk 59 formed in ongoing
starbursts fuelled by a huge gas inflow, turning the galaxy into an asymmetric
`green pea' or blue compact dwarf. We map the HeII$\lambda4686$ emission, and
identify a broad component from the central nebula, consistent with the
emission of $\sim 300$ Wolf-Rayet stars. About a third of the HeII$\lambda$4686
flux is a narrow line emitted from a more extended area covering the central
and spur nebulae, and may have a different origin.
