I found many discussions online regarding the harmonic analysis of Antonio Carlos Jobim’s Girl From Ipanema. Here’s my two cents.
There is some confusion with the second chord in the A section and the first four bars on the bridge.
The second chord in the A section is often (and inaccurately) analyzed as a V/V. However it is a II7. The reason is that this chord is not aiming at resolving to the V, but it goes somewhere else. There are a few kinds of II7. In Girl From Ipanema is a II7 with a Lydian b7 chord-scale. It gives a distinct Brazilian sound to the progression.
The first 4 measures on the bridge are often (and again inaccurately) analyzed as Imaj7-IV7. This passage is actually in the key of Gb and the analysis is IVmaj7 (Lydian)-bVII7 (Lydian b7). It is one of those modulations where the I is never used. Brilliant.
On a separate note, it’s very interesting to compare the A sections of Girl From Ipanema and Take the A Train. We will address on a separate blog post.