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As one of the most active blazars, Mrk421 is an excellent candidate for thestudy of the physical processes within the jets of AGN. Here we report on theextensive multi-wavelength observations of Mrk 421 over 4.5 years, from 2008August to 2013 February. This source was simultaneously monitored by severalexperiments at different wavelengths: ARGO-YBJ in TeV $\gamma$-rays,$Fermi$-LAT in GeV $\gamma$-rays, $Swift$-BAT in hard X-rays, $RXTE$-ASM,$MAXI$ and $Swift$-XRT in soft X-rays, $Swift$-UVOT in ultraviolet, and OVRO inradio frequencies. In particular, thanks to the ARGO-YBJ and $Fermi$ data, thewhole energy range from 100 MeV to 10 TeV is covered without any gap.  According to the observed light curves, ten states (including seven largeflares, two quiescent phases and one outburst) were selected. For the firsttime, the multi-wavelength spectral evolutions of Mrk 421 during differentstates were systematically analyzed. During the outburst phase and the sevenflaring episodes, the peak energy in X-rays is observed to increase fromsub-keV to few keV. The TeV $\gamma$-ray flux increases up to 0.9$-$7.2 timesthe flux of the Crab Nebula. The behavior of GeV $\gamma$-rays is found to varydepending on the flare, a feature that leads us to classify flares into threegroups according to the GeV flux variation. Finally, the observed radiationspectra above 0.3 keV of different states can be reasonably described by asimple one-zone synchrotron self-Compton model. The underlying physicalmechanisms responsible for different states may be related to the accelerationprocess or to variations of the ambient medium.

4.5-year simultaneous multi-wavelength observation of Mrk 421 in the ARGO-YBJ and Fermi overlap era