This thesis “Simulations of free-floating planet detection with microlensing” is written by Makiko Ban and submitted to the University of Manchester for a degree of PhD in astronomy and astrophysics in 2016.Free-floating planets (FFPs) are very difficult to observe directly since they are isolated and intrinsically faint. The gravitational microlensing effect is now major method to observe FFPs, but observing low-mass FFPs is still difficult due to their short duration. We compute simulations for FFP microlensing observations down to Earth-mass using the numerical Besancon Galactic model created by Robin et al. (2012a). These are the first detailed simulation of FFP microlensing using a population synthesis Galactic model incorporating a 3D extinction model, and we also take full account of finite source effects. Firstly, we simulate the microlensing event rate and spatial distribution using three different modes, and for each mode three FFP lens masses (Jupiter, Neptune, and Earth). For the target area of (l, b) =(1, -1.75) which corresponds to the centre of the proposed Euclid ExELS field, our simulations result in 184-920 Jupiter-mass FFPs during the 5 year Euclid mission depending on simulation assumptions. For the Earth-mass FFPs, the rate range is 9-49 FFPs assuming 100% detection efficiency. Next, we compute the rate of parallax detection using a 3D model of the observers. We consider parallax detection by Euclid and WFIRST-AFTA, and by Euclid and LSST. We found that 52 Jupiter-mass FFPs will be detected by a parallax between Euclid and WFIRST-AFTA for two 30-day continuous period around equinoxes if they observe simultaneously. The rate falls to 4 parallax events for Earth-mass FFPs. The parallax detection between Euclid and LSST would be affected by the observation time on the Earth, but it could provide 20 Jupiter-mass FFPs down to 1.4 Earth-mass FFPs.