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Preterm infants may spend months in the neonatal intensive care unit. During this time, their brain wires itself for the rest of their lives. Any adverse events related to neurological illness or challenges in treatment may disturb this process. This Thesis develops methodology for bedside monitoring of brain function in preterm infants by electroencephalography (EEG). The main feature of preterm EEG is intermittently occurring spontaneous activity transients (SAT), which drive the development of neuronal connections. The work in this Thesis developed and optimized an algorithm that automatically detects these events from EEG. Further, it is shown that measures based on SAT detection have clinical correlates. The methodology may contribute to better brain care of preterm infants by providing real time information about brain health to treating clinicians. K irsi P alm u E v en t d etectio n in p reterm electro en cep h alo grap h