1 INTRODUCTION
2 THE DATA: PANCHROMATIC OBSERVATIONS OF ELAIS-N1, BOÖTES AND THE LOCKMAN HOLE
2.1 Radio observations with LOFAR
2.2 Multi-wavelength data
2.3 A cross-matched radio and photometric catalogue
2.4 Deriving photometric redshifts of LOFAR-identified sources
2.5 Classification of star-forming galaxies and AGN
2.6 Stellar masses and star formation rates for star-forming galaxies
3 THE RADIO LUMINOSITY FUNCTION OF STAR-FORMING GALAXIES
3.1 Constructing the 150 MHz luminosity function
3.2 Radio completeness corrections
3.3 Incorporating uncertainties in photometric redshifts
3.4 Parametric fits to the radio luminosity function
4 RELIABLE CONVERSION OF $L_{150\mathrm{MHz}}$ TO SFR
4.1 The star formation rate function constructed using different SFR estimates
4.2 The impact of the calibration between radio luminosity and SFR
5 THE COSMIC STAR FORMATION DENSITY HISTORY
5.1 The functional form of the SFRD
5.2 Comparison to literature data
5.3 Comparison to models of galaxy formation
5.4 Further work
6 CONCLUSIONS