Scales to Play Over Am
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A Am chord contains the notes A – C – E. Any scale that includes every one of those 3 tones fits over it — from the root A, that means A Natural Minor, A Melodic Minor, A Harmonic Minor, A Minor Pentatonic, A Blues, A Rock 'n' Roll, A Dorian, A Phrygian, A Dorian Bebop, A Half Whole Diminished, A Gypsy Major and A Gypsy Minor. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
Am is also diatonic to 3 major keys: C major (relative minor Am), F major (relative minor Dm), G major (relative minor Em). In a song from one of those keys you can also solo with the key's own major scale or its relative minor pentatonic across the whole progression, not just this chord.