even; so much as; not even
さえ marks an extreme example, meaning 'even' or 'not even', and can also mean 'so much as' in negative contexts.
さえ highlights one item as an extreme example, suggesting that if even that is true or possible, then less extreme cases are obvious. In negative sentences it means 'not even' or 'so much as', emphasizing that the minimum action or thing did not happen. For example, 漢字さえ読めない means 'can't even read kanji', implying nothing more advanced is possible.
With verbs, さえ can combine with the て-form to mean 'even doing' or with the ます-stem plus する to mean 'even go so far as to'. It also appears in conditional patterns like さえあれば or さえすれば, meaning 'if only' — this is a common N3 usage.
さえ often replaces the particles が or を, but can follow other particles such as で, に, と. In formal writing, ですら is a near-synonym, but in conversation さえ is more common and can sound slightly emphatic.