The low frequency regime (less that 300 MHz) of radio astronomy, while been its birthplace, has been neglected in the past several decades due to the challenges of calibration. External galaxies have hardly been observed at these frequencies with several exceptions. Such observations always suffered from poor angular resolution and therefore accurate flux measurements were nearly impossible. In addition virtually no research in polarization has been performed at these frequencies due to various physical and instrumental depolarization processes. Observing external galaxies at low frequencies would enable us to study the propagation of low energy electrons and in turn weak magnetic fields. Thankfully, a revival in low frequency radio astronomy is now in full force with interferometers such as the GMRT being constructed. This is especially so with the construction of the Low Frequency Array (LOFAR) which officially opened in 2012. This thesis took place during the commissioning phase of LOFAR and therefore contains many technical commissioning tasks mainly addressing the calibration of LOFAR data which were essential for the wider community. This includes developing software to interpolate gain solutions in frequency, enabling more bandwidth on the observational target and thus increasing sensitivity. This thesis presents the first arcsecond observations of nearby galaxies at low frequencies with LO- FAR. We mapped the face-on interacting galaxy M51 and the edge-on galaxy NGC891 to study the propagation of low energy cosmic ray electrons especially in the extended disk and halo. We also employ the novel method of RM synthesis to search for linear polarization in these galaxies and their surrounding fields for polarized background sources. In M51 we observe no break in the integrated spectrum but there are signs of thermal absorption in center of the galaxy. We observe a radial break of the radio continuum emission beyond M51’s star forming disk, demonstrating that detecting the extended disk in radio contiuum will still be difficult even at low frequencies. We have created a program to model the cosmic ray electron distribution for M51 and we find that a diffusion coefficent of approximately 7.5 × 1028 cm2 s-1 is needed to describe the radial spectral index of M51. From these models we can also determine the thermal fraction in the center of M51 and spiral arms at 151 MHz. We also see that the magnetic field in the outer disk obtained from observations are underestimated due to assumptions made using equipartition. Through this observation and model we conclude that diffusion is the dominate process in the cosmic ray electron propagation in M51. The observed frequency dependence of radial scalelengths and the radio-infrared correlation of M51 both confirm our diffusion model. In M51 and NGC891, no diffuse linear polarization was detected showing that detecting diffuse po- larization in star forming galaxies at low frequencies will be impossible at current sensitivities. In the M51 field, we detect six polarized extragalactic sources, resulting in a polarization detection for every 2.9 square degrees, making previous plans of using RM grids of background polarized sources to probe the weak magnetic fields of nearby galaxies quite unrealistic. We confirm the spectral break in NGC891 seen in previous studies and we observe significant signs of thermal absorption within the disk of NGC891. We argue that increased thermal absorption by classical HII regions due to the path length and hence inclination causes the flatting of the integrated spectral index at low frequencies. Also it is found that a low temperature ionized gas component as proposed by Israel & Mahoney (1990) is not needed to explain the thermal absorption. We detect the supernova SN1986J at 146 MHz with a peak flux of 8.8 mJy. We observe significant outflows in the halo via the spectral index map and also observe a new feature not seen in higher frequencies, possibly created via increased star formation in the disk. We see that the bulk velocity of the galactic wind speed is relatively constant for only one half of the galaxy making NGC891 different from NGC253. New observations of the nearly face on galaxy NGC628 were also taken with the Effelsberg 100m telescope and the Jansky Very Large Array in order to detect rotation measure gradients signifying outflows from the disk to the halo of the galaxy. Preliminary results do detect such RM gradients and reversals. Finally this thesis also contains work done on the calibration and processing of the MSSS (Multi Frequency Snapshot Survey) survey for which linear polarization was detected, thus opening up the first low frequency polarization survey of the entire northern sky
