1 Introduction

Mrk 421 is the brightest BL Lac object at X-ray and UV wavelengths and it is the first extragalactic source discovered at TeV energies (Punch et al. 1992). This nearby (z = 0.031) X-ray bright BL Lac has been observed by essentially all previous X-ray missions and shows remarkable X-ray variability correlated with strong activity at TeV energies (e.g., Takahashi et al. 1996; Maraschi et al. 1999). BL Lacs are thought to be dominated by relativistic jets seen at small angles to the line of sight (Urry & Padovani 1995), and their radio-through-X-ray spectra are well fitted by inhomogeneous jet models (Bregman et al. 1987). However, the structure of the relativistic jets remains largely unknown as the models are generally under-constrained by single epoch spectra and the typical smooth and nearly featureless blazar spectra can be reproduced by models with widely different assumptions (e.g., Königl 1989). Combining spectral and temporal information greatly constrains the jet physics. Time scales are related to the crossing times of the emission regions which depend on wavelength and/or the time scales of micro-physical processes like acceleration and radiative losses. The measured lags between the light curves at different energies as well as spectral changes during intensity variations allow to probe the micro-physics of particle acceleration and radiation in the jet. Thus XMM-Newton with its high sensitivity and broad energy bandwidth is an ideal tool to study BL Lacs as it allows spectroscopy with unprecedented time resolution, uninterrupted by gaps because of the long period of the satellite orbit. Mrk 421 was the first BL Lac object to be established as an X-ray source (Ricketts et al. 1976; Cooke et al. 1978) and subsequent observations indicated that the X-ray spectrum has a soft power law form (Mushotzky et al. 1978; Hall et al. 1981) which exhibits significant variability (Mushotzky et al. 1979). More detailed studies with IUE and EXOSAT showed that the variability occurs on time scales of typically a day with an e-folding time scale of $\sim$5 10⁴ s (George et al. 1988). The source shows a dichotomy of X-ray states: a low, soft state ( $f_{2-6~{\rm keV}} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$ } 2~10^{-11}$ erg cm^-2 s^-1, $\Gamma \sim 2.8$) where the source hardens when it brightens and a hard outburst state ( $f_{2-6~{\rm keV}} \lower.5ex\hbox{$\; \buildrel > \over \sim \;$ }8~10^{-11}$ erg cm^-2 s^-1) during which the spectral index remains at $\Gamma \sim 2$. In several Ginga observations, partly simultaneously with ROSAT, Mrk 421 was found at intermediate fluxes of $f_{2-6~{\rm keV}} = (3.6 - 5.2)~10^{-11}$ erg cm^-2 s^-1 (Makino et al. 1992; Tashiro 1994). The data indicated that the amplitude of the flux variations with time scales of a few hours got larger with increasing energy and the correlation between flux and spectral index was inconsistent with that observed by EXOSAT. The quality of the spectral fits improved considerably by using a broken power law or a power law with exponential cut off and the Ginga spectrum was significantly steeper than the simultaneous ROSAT spectrum. Since its discovery as a TeV source several multi-wavelength campaigns have been conducted to study possible time lags between the X-ray band and TeV energies and to investigate the pronounced spectral evolution during flares seen in X-rays with ASCA and BeppoSAX (Macomb et al. 1995, 1996; Takahashi et al. 1996; Fossati et al. 1998; Maraschi et al. 1999). The source generally shows a complex behavior. While Takahashi et al. (1996) found a lag of about 4000 s between the soft (0.5-1.0 keV) photons and the hard band (2-7.5 keV), which was interpreted as an effect of radiative cooling, recent ASCA observations show both, positive and negative lags (Takahashi et al. 2000). BeppoSAX observations of a flare in April 1998, simultaneously observed at TeV energies, showed that the hard photons lag the soft ones by 2-3 ksec and that, while the light curve is symmetric at softest X-ray energies, it becomes increasingly asymmetric at higher energies with the decay being slower than the rise (Fossati et al. 2000). Fitting the ASCA data by a simple power law Takahashi et al. (1996) find that an absorbing column density considerably higher than the Galactic value of $N_{\rm H} = 1.5~10^{20}$ cm^-2 (Elvis et al. 1989) is required to obtain acceptable fits. Fixing the absorption at the Galactic value a broken power law model provides a better fit than a simple power law, but the $\chi^2_{\rm red}$ is often un-acceptable. With these models the break energy is at $\sim$1.5 keV, and the change of the power law index at the break point is $\Delta \Gamma \sim 0.5$. With the wider energy range of BeppoSAX it became clear that these simple models are not adequate descriptions of the downward curved Synchrotron spectra (Fossati et al. 2000) and continuously curved shapes had to be employed (Inoue & Takahara 1996; Tavecchio et al. 1998). The Synchrotron peak energy varied between 0.4-1 keV, the spectral index at an energy of 5 keV between $1.5 \leq \alpha \leq 2.2$. Both quantities are correlated with the X-ray flux: the peak energy positively, the spectral slope inversely: with increasing flux the synchrotron peak shifts to higher energies and the spectrum at 5 keV gets flatter. Most of these results were obtained from data integrated over wide time intervals (typically one satellite orbit) and from giant flares with time scales of a day. Uninterrupted data with high temporal and spectral resolution can only be provided by XMM-Newton with its high sensitivity, spectral resolving power, and broad energy band.