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Galaxies are among nature's most majestic and diverse structures. They can play host to as few as several thousands of stars, or as many as hundreds of billions. They exhibit a broad range of shapes, sizes, colours, and they can inhabit vastly differing cosmic environments. The physics of galaxy formation is highly non-linear and involves a variety of physical mechanisms, precluding the development of entirely analytic descriptions, thus requiring that theoretical ideas concerning the origin of this diversity are tested via the confrontation of numerical models (or "simulations") with observational measurements. The EAGLE project (which stands for Evolution and Assembly of GaLaxies and their Environments) is a state-of-the-art suite of such cosmological hydrodynamical simulations of the Universe. EAGLE is unique in that the ill-understood efficiencies of feedback mechanisms implemented in the model were calibrated to ensure that the observed stellar masses and sizes of present-day galaxies were reproduced. We investigate the connection between the morphology and internal kinematics of the stellar component of central galaxies with mass M* > 10^9.5 Msun in the EAGLE simulations. We compare several kinematic diagnostics commonly used to describe simulated galaxies, and find good consistency between them. We model the structure of galaxies as ellipsoids and quantify their morphology via the ratios of their principal axes. We show that the differentiation of blue star-forming and red quiescent galaxies using morphological diagnostics can be achieved with similar efficacy to the use of kinematical diagnostics, but only if one is able to measure both the flattening and the triaxiality of the galaxy. Flattened oblate galaxies exhibit greater rotational support than their spheroidal counterparts, but there is significant scatter in the relationship between morphological and kinematical diagnostics, such that kinematically-similar galaxies can exhibit a broad range of morphologies. The scatter in the relationship between the flattening and the ratio of the rotation and dispersion velocities (v/σ) correlates strongly with the anisotropy of the stellar velocity dispersion: at fixed v/σ, flatter galaxies exhibit greater dispersion in the plane defined by the intermediate and major axes than along the minor axis, indicating that the morphology of simulated galaxies is influenced significantly by the structure of their velocity dispersion. The simulations reveal that this anisotropy correlates with the intrinsic morphology of the galaxy's inner dark matter halo, i.e. the halo's morphology that emerges in the absence of dissipative baryonic physics. This implies the existence of a causal relationship between the morphologies of galaxies and that of their host dark matter haloes. Using these tools, we also investigate the morphology and kinematics of central galaxies with mass M* > 10^9.5 Msun and their globular cluster (GC) populations in the EAGLE spinoff project E-MOSAICS that incorporates the MOSAICS model of stellar cluster formation and evolution. We find that metal-poor and metal-rich GC populations (split by a threshold at [Fe=H] = -1) exhibit differing characteristic morpho-kinematic properties. The former are significantly more elliptical and dispersion-supported than the latter. In detail, the relations connecting the kinematic properties of the populations with those of their host galaxy exhibit good agreement with available observations, with the velocity dispersions of both metal-poor and metal-rich GC populations correlating positively with that of the host galaxy. The rotational velocity of the metal-rich globular cluster population also correlates positively with that of the host galaxy. The relationship between the morpho-kinematics of the metal-rich globular clusters and the host galaxy's field stars exhibits a scatter that is sensitive to the relative ages of the two populations: for fixed globular cluster kinematics, the field star population is more disky/rotation-supported if they are younger. We confirm that the connection between the morpho-kinematics of galaxies and their velocity dispersion anisotropy revealed in EAGLE is also exhibit in the higher-resolution E-MOSAICS simulation. However, the same behaviour is not seen in the metal-rich globular clusters, which we speculate is a consequence of them not representing a self-gravitating system.

The galaxy within which we reside, the Milky Way, offers perhaps the highest fidelity training ground for models of galaxy formation, providing insights into its history of formation and evolution on a star-by-star basis. Such insights are only truly useful for constraining disc galaxy formation models if we properly understand the wider context of the Milky Way among the plethora of galaxies in the Universe. This thesis aims to make progress toward answering the question of whether the Milky Way is a typical disc galaxy. Through the effort to answer this question, this thesis presents new measurements of the structure of our Galaxy and new insights into aspects of its history of assembly and evolution which have a strong influence on its α-element abundances. Providing a baseline constraint on future models for the formation of the Galaxy, I present a dissection of the Milky Way disc spatial structure as a function of [Fe/H], [α/Fe] and stellar ages (based on the surface abundances of Carbon and Nitrogen), as measured by the APOGEE survey. I measure the disc density profile, fitting the scale heights and lengths of mono-age, mono-[Fe/H] sub-populations in the high and low [α/Fe] disc. The fitted disc vertical scale height distribution is smooth when weighted by surface-mass density, suggesting that the high and low [α/Fe] populations are not vertically distinct at the solar radius, as would be expected if they were interchangeable with the geometric thin and thick disc components. I find that the surface density profile of low [α/Fe] mono-age, mono-[Fe/H] populations is best fit by a broken exponential, such that their density increases with R to a peak radius, and declines thereafter, whereas the high [α/Fe] populations are better described by a single, declining exponential within the range of Galactocentric radii observed by APOGEE. The trends of the density profile parameters as a function of age and metallicity provide insights into the structural evolution of the Galaxy, and provide strong constraints on future models of its formation and evolution. In particular, a main finding of this study is that the high and low [α/Fe] discs have a relatively distinct radial structure. To understand the origin of the structures found in the above study, and to generate novel and predictive models for the formation of the Galaxy, I perform an analysis of element abundances in Milky Way like galaxy discs in the EAGLE simulation. I concentrate on the abundance of α-elements in these galaxies, with a view to understanding the origin of the bimodality in [α/Fe] at fixed [Fe/H] which is apparent in both the Milky Way and in EAGLE Galactic analogues. I show that EAGLE reproduces broad expectations for the production of α-elements from simple chemical evolution models, namely that stars with enhanced [α/Fe] are born from gas in rapidly star forming environments at high density. These environments are conducive to forming α-enhanced stars because their gas consumption timescale is considerably shorter than the characteristic delay timescale for Type Ia supernovae. I further show that such environments are only achieved in EAGLE haloes when the rate of dark matter accretion is faster at early times than the majority of galaxies with similar stellar mass at z=0. The necessity for this atypical and rapid early assembly means that galaxies hosting discs with [α/Fe] bimodality are extremely rare, forming in ≈ 6% of galaxies at the Milky Way stellar mass range. Following the prediction of EAGLE that galaxies which host [α/Fe] bimodality like that of the Milky Way should have atypical histories of assembly, I then perform a study of Milky Way halo stars in common between APOGEE and Gaia DR2, with a view to placing constraints on the accretion history of the Galaxy. I present a detailed characterisation of the kinematics and abundances of the recently discovered Gaia-Enceladus association, which is proposed to be the debris of a singular and massive accretion event. By comparing the kinematics and abundances of Gaia-Enceladus to the debris of satellites accreted onto Milky Way analogues in the EAGLE simulations, I make a quantitative prediction of the stellar mass of the Milky Way satellite to be 10^8.5 < M* < 10^9 Msun and predict its earliest possible time of accretion to be z≈1.5. I also show that such mergers are uncommon in the simulations, in agreement with the prediction that the Milky Way assembly history should be atypical. The above results outline a new view of the Galaxy in which it is potentially not a good example of a `typical' disc galaxy, playing host to structural components which are linked to its chemistry in a complex manner, which may indicate that its history of assembly is not in common with other galaxies at the same stellar mass. In finding that the Galaxy is atypical in this way, this thesis has uncovered new aspects of the evolutionary history of the Milky Way, which pave the way for future work towards the goal of fully reconstructing the history of our Galaxy and using that understanding to formulate robust and general models for the formation of disc galaxies.