The first study year is very decisive in terms of a smooth transition into and engagement with university education. The main goal of this study is to develop a multidimensional model for assessing student engagement and use it with first-year students in a research-intensive university in Finland. Based on theoretical modelling and three-step piloting, an online Nexus self-assessment questionnaire was designed and used to conduct an annual survey of first-year students from 2013 to 2018 in the target university. A total of 1936 first-year students from different disciplinary fields responded. Three different engagement clusters were observed, with each representing a very different student relationship with engagement and learning. Academically engaged students showed a very balanced relationship with academic orientation in terms of their studies and study-related communities, whereas non-academically engaged students revealed tendencies towards certain knowledge-seeking and task-avoidance behaviours. Loosely engaged students seemed to also have a shallower academic orientation and, in addition, a weaker relationship with study-related communities. The three identified engagement clusters were also distributed differently within disciplinary fields. As an implication of the study, the way in which academic teaching and learning communities at the studied institution can benefit from the engagement assessment results and offer more focused support to students is discussed.