The Milky Way galaxy, like all spiral galaxies, is surrounded by a roughly spherical distribution of stars called the halo. The halo was largely formed when the galaxy merged with smaller galaxies. The stellar population of the inner halo is dominated by debris from one major such merging event, called the Gaia-Enceladus-Sausage, and the outer halo population is completely built up by several mergers. To properly understand this accretion history, the halo needs to be investigated out to large distances so that as much substructure as possible can be traced. The substructure is expected to leave an imprint in the halo's metallicity structure. In this thesis, we use a catalogue of intrinsically bright stars, giants, to probe the metallicity structure of the halo to large distances. It contains 205,727 stars that all have photometric metallicities from the Pristine survey and distances derived from isochrone fitting, and reaches down to [Fe/H] = -4.0 dex and out to d = 96.16 kpc. Its purity is 90 % and completeness is 67 %. We calculate the distance errors by Monte Carlo simulations and introduce a new cut in colour that is dependent on metallicity to reduce contaminants in the sample. This introduces a metallicity bias in the sample that we can correct for because we coupled metallicity and colour. The correction is done by computing weights for different metallicity bins. The final catalogue allows us to create metallicity distribution functions of the halo as a function of distance. These show us that as heliocentric distance, the distance from the Galactic centre or the Galactic plane increases, the overall metallicity decreases. At the closest distances, the thick disk metallicity peak at -0.7 dex dominates, but as we move further out this smoothly shifts to -1.3 dex and then to -1.6 dex, representing the inner halo, while a peak at -2.2 dex, representing the outer halo, starts to become visible beyond 6 kpc and dominates the metallicity distribution past 26 kpc. These peaks are remnants of merger events in the halo, with the inner halo peak being due to the massive Gaia-Enceladus-Sausage merger and the outer halo peak being due to the many, low-mass and thus low-metallicity galaxies accreted there. We are able to see signals from the Sagittarius stream and Gaia-Enceladus-Sausage's apocentric pile-ups in the metallicity distribution functions, showing that the halo's metallicity changes with not only distance but also sightline. We also detect a diffuse, very metal-poor cloud in the southern footprint that may be an until now unknown structure. This catalogue and its resulting metallicity distribution functions are thus a suitable addition to literature at the metal-poor and distant end, as well as the faint end where e.g. Gaia mission data is unable to provide metallicities and distances. / Vintergatan är, som alla spiralgalaxer, omringad av en ungefärligen sfärisk distribution av stjärnor som kallas halon. Denna halo bildades när galaxen sammansmälte med mindre galaxer. Stjärnpopulationen i den inre halon domineras av stjärnor som kom in med en sådan, väldigt stor, sammanslagning med en annan galax som eter Gaia-Enceladus-Sausage, och den yttre halons stjärnpopulation har helt och hållet byggts upp av sammanslagningar med flera galaxer. För att kunna kartlägga Vintergatans alla sammanslagningar med andra galaxer behöver vi därför undersöka den yttre halon så långt ut som möjligt, för att spåra så mycket substruktur i halon som uppstod till följd av sammanslagningar som möjligt. Sådan substruktur förväntas göra ett avtryck i halons metallicitetsstruktur. I denna masteruppsats används en katalog av intrinsiskt ljusstarka stjärnor, jättar, för att kartlägga halons metallicitetsstruktur till stora avstånd. Katalogen innehåller 205,727 stjärnor som alla har fotometriska metalliciteter från Pristine-undersökningen samt avstånd från isokronanpassning. Den når [Fe/H] = -4.0 dex och d = 96.16 kpc. Mängden jättar i katalogen är 90 % och katalogen behåller 67 % av alla jättar i ursprungskatalogen. Avståndens osäkerhet beräknas med Monte Carlo-simulationer, och det införs ett nytt klipp med färg som är beroende av metallicitet för att undvika kontamination. Detta inför en metallicitetssnedvridning av katalogen som vi kan korrigera eftersom att vi kopplade ihop metallicitet och färg. Korrektionen sker genom att vi beräknar vikter för olika metallicitetsintervall i katalogen. Den slutgiltiga katalogen låter oss skapa metallicitetsdistributioner för halon som beror på avstånd. Dessa distributioner visar oss att när stjärnors avstånd till solen, från galaxens centrum samt från galaxdisken ökar, så minskar den genomsnittliga metalliciteten. Vid väldigt nära avstånd är distributionerna centrerade runt -0.7 dex som motsvarar den tjocka disken, men när avstånden ökar, flyttas denna topp till -1.3 dex och sedan till -1.6 dex, vilket motsvarar den inre halon, samtidigt som en topp vid -2.2 dex, som motsvarar den yttre halon, framträder bortom 6 kpc och dominerar metallicitetsdistributionen för halon bortom 26 kpc. Dessa toppar är kvarlevor efter sammanslagningar mellan Vintergatan och mindre galaxer, där toppen i den inre halon uppstod p.g.a. Gaia-Enceladus-Sausage och toppen i den yttre halon kommer från de många lågmassiva och därmed metallfattiga dvärggalaxer som assimilerats där. Metallicitetsdistributionerna visar signaler från Sagittariusströmmen och Gaia-Enceladus-Sausages apocentriska hopsamlingar, vilket visar att halons metallicitet inte bara beror på avstånd utan även på observationsvinkel. Katalogen visar spår av ett diffust metalfattigt moln i det södra observationsfönstret som potentiellt är en hittills oupptäckt struktur. Denna katalog och dess resulterande metallicitetsdisitributioner är en viktig addering till existerande litteratur i den metallfattiga och avlägsna regimen, samt i den ljussvaga regimen där t.ex. data från Gaiateleskopet inte kan bidra med metallicitets- eller avståndsvärden.

The Milky Way's halo is an approximately spherical distribution of stars surrounding the Galaxy that carries the history of the Milky Way. The outer halo is a Galactic region with long dynamical timescales largely built up by accreted material. Probing its stellar constituents has been historically difficult due to the distances of outer halo stars, making them appear faint. To characterise the distant halo and unravel the history of our galaxy, we thus need to use stars that are intrinsically bright, i.e. giant stars. To draw useful conclusions about the distant halo, these target giants should have metallicity and kinematics information. Therefore a catalogue of distant halo giants with Pristine survey metallicities, Gaia mission data and distances has been created in this work. The cuts used to create this catalogue are made to remove as many dwarf stars as possible and have been tested on a training sample containing spectroscopic metallicities and surface gravities as well as Gaia mission data. Defining giants as being all stars with log(g) < 3.5 dex, we can calculate the purity and completeness of the sample after the cuts have been applied to test which cuts optimise the catalogue. The methods used to cut away the dwarfs are to first plot all stars with positive Gaia parallaxes and fractional parallax uncertainties smaller than 50% in a colour-absolute magnitude diagram and remove all stars from the sample that in this plot populate the main sequence. We then colour-code the colour-apparent magnitude diagram by purity and completeness after this parallax cut has been performed, and select a region in this diagram in which both purity and completeness are maximised, with the final region being (GBP,0 - GRP,0) > 0.8 and G0 < 17.6. The distances to the stars in this region are then computed by comparing their apparent magnitudes to the absolute ones of isochrones. These cuts are then applied to a sample of 6,884,547 stars with Pristine survey and Gaia mission data. The final catalogue is kinematically unbiased and contains 345,303 halo giants. It contains 78% giants and only 4% of giants are erroneously deselected.  With the final sample we are able to probe as deep as 103 kpc into the halo and have created preliminary metallicity distribution functions of different regions of the halo. This sample will be used to further investigate the distant halo metallicity structure and its substructure that was created through merger events.