The second half of the first part begins as indicated on an E minor 7th chord (in this case a nice voicing with the option note F#, i.e. the ninth). Now comes an unusual compositional trick: the harmonies are directed to B flat major via the intermediate dominant F#7. One would normally expect the parallel minor chord of B flat minor here, but Tom Jobim manages to incorporate this unusual key change almost effortlessly. Two more intermediate dominants follow: B7(b9) leads to E7(9), the double dominant.
Before it goes into the repetition, the composer has reserved a nice chord. At first glance, the EbMaj7 chord is unusual in the key of D major. However, it is a usual harmonic suspension in jazz to insert the chord of the diminished second degree (also as a major7 chord) before the return to the tonic.
There follows a repetition of the first part and then a long second part in which there are two more key changes, many secondary dominants and other borrowed chords to discover.