There are 10 Glyphs to find throughout Roma. The order you find them in does not matter in terms of the order of the puzzles within them.
Here's a video showing how to beat all of the puzzles as well as screenshots displaying the locations on the map. I did these after beating the main story.
In terms of the Ring Puzzles, the "RING 1" refers to the ring(s) you start on.
#1 - 0:12 Castra Praetoria
#2 - 1:09 Rosa in Fiore
#3 - 3:17 Castel Sant'Angelo
#4 - 4:33 Santa Maria dei Miracoli and Santa Maria di Montesant
#5 - 6:03 Caserma di Alviano
#6 - 7:25 Aventino
#7 - 9:08 Acquedotto Claudia
#8 - 11:03 Colosseo
#9 - 12:41 Palazzo Senatorio
#10 - 14:13 The Pantheon