These are the syllabus steps for the Foxtrot, as listed in the British Dance Council Rulebook here.
Videos are by Brett Long, Ballroom Guide, Egils Smagri, iDanceTW and Syllabus Dance-Sport - many thanks for these excellent resources! Step descriptions can also be found on Ballroom Guide here.
Nomenclature
Walk
Feather Step
Three Step
Natural Turn
Reverse Turn
Change of Direction
Closed Impetus and Feather Finish Impetus Turn
Natural Weave
Basic Weave
Weave after 1-4 Reverse Wave
Reverse Wave
Closed Telemark - Telemark
Open Telemark, Feather Ending
Top Spin - Top Spin after Feather Finish (all alignments)
Hover Feather
Hover Telemark
Natural Telemark
Hover Cross
Open Telemark, Natural Turn, Outside Swivel, Feather Ending
Open Impetus Turn
Weave from PP
Natural Twist Turn
Reverse Pivot
Quick Open Reverse
Quick Natural Weave from PP
Curved Feather to Back Feather
Curved Feather
Back Feather
Curved Feather from PP
Natural Zig-zag from PP
Fallaway Reverse & Slip Pivot
Natural Hover Telemark
Bounce Fallaway with Weave ending
Extended Reverse Wave
Curved Three Step