In this thesis, multiple ionisation processes of free atoms and molecules upon single photon absorption are studied by means of a versatile multi-electron-ion coincidence spectroscopy method based on a magnetic bottle, primarily in combination with synchrotron radiation. The latter offered the possibility to access not only valence but also core levels, revealing processes, which promote the target systems into different charge states. One study focuses on double and triple ionisation processes of acetaldehyde (ethanal) in the valence region as well as single and double Auger decay of initial 1s core vacancies. The latter are investigated site-selectively for the two chemically different carbon atoms of acetaldehyde, scrutinising theoretical predictions specifically made for that system. A related study concentrates on core-valence double ionisation spectra of acetaldehyde, which have been investigated in the light of a previously established empirical model, and which have been used as test cases for analysing this kind of spectra by means of quantum chemical electronic structure methods of increasing sophistication. A third study investigates site-specific fragmentation upon 1s photoionisation of acetaldehyde using a magnetic bottle augmented with an in-line ion time-of-flight mass spectrometer. Experimental evidence is presented that bond rupture occurs with highest probability in the vicinity of the initial charge localisation and possible mechanisms are discussed. A site-specificity parameter P∆ is introduced to show that differences in fragmentation behavior between initial ionisations at chemically different carbon atoms probably persist even for identical internal energy contents in the nascent dications. In another study where both electrons and ions from Auger decay of core-excited and core-ionised states of CO2 are detected in coincidence, it is confirmed that O2+ is formed specifically in Auger decay from the C1s → π* and O1s → π* resonances, suggesting a decisive role of the π* orbital in the molecular rearrangement. Also, the molecular rearrangement is found to occur by bending in the resonant states, and O2+ is produced by both single and double Auger decay. A new version of the multi-electron-ion coincidence method, where the ion time-of-flight spectrometer is mounted perpendicularly to the electron flight tube, which affects less the electron resolution and which allows for position sensitive detection of the ions, is employed in combination with tunable soft X-rays to reveal the branching ratios to final Xen+ states with 2 &lt; n &lt; 9 from pure 4d-1, 4p-1, 4s-1, 3d-1 and 3p-1 Xe+ hole states. The coincident electron spectra give information on the Auger cascade pathways. / <p>Byte av lokal vid disputation till Polhemssalen.</p>