The development and characterisation of a multichannel extreme-UV (XUV) spectrometer system for emission and absorption spectroscopy of laser produced plasmas is described. The system consists of a 2.2m grazing incidence vacuum spectrometer to which an XUV sensitive array detector is coupled. The multichannel detector consists of a Galileo® Channel Electron Multiplier Array (CEMA) with Photodiode Array (PDA) readout. A comprehensive and user friendly software package for array detector/ experiment control and data acquisition was developed. The total system performance is illustrated by emission spectra of aluminium, aluminium oxide and tungsten and photoabsorption spectra of helium gas and thin aluminium samples. Limitations of the current system for the measurement of photoabsorption cross-sections are discussed. The fundamental principles underlying three important classes of deconvolution methods, Fourier, Constrained Non-Linear and Maximum Likelihood, are described. The results of computer codes developed to implement each of the above techniques are presented and intercompared. Strengths and weaknesses of each technique are discussed with reference to restored emission spectra. The potential of deconvolution for resolution gain is demonstarted by application to an instrumentally broadened He ls2 - 2s2p doubly excited resonance profile. The thesis concludes with a description of future work on system characterisation and optimsation.