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
Forward and Backward Walk TechniqueFeather Step
Feather StepThree Step
Three StepNatural Turn
Natural TurnReverse Turn
Reverse Turn and Feather FinishChange of Direction
Change of DirectionClosed Impetus and Feather Finish Impetus Turn
Closed Impetus and Feather FinishNatural Weave
Natural WeaveBasic Weave
Basic WeaveWeave after 1-4 Reverse Wave
Weave after 1-4 Reverse WaveReverse Wave
Reverse WaveClosed Telemark - Telemark
Closed TelemarkOpen Telemark, Feather Ending
Open Telemark and Feather EndingTop Spin - Top Spin after Feather Finish (all alignments)
Top SpinHover Feather
Hover FeatherHover Telemark
Hover TelemarkNatural Telemark
Natural TelemarkHover Cross
Hover CrossOpen Telemark, Natural Turn, Outside Swivel, Feather Ending
Open Telemark, Natural Turn, Outside Swivel, Feather EndingOpen Impetus Turn
Open Impetus TurnWeave from PP
Weave from PPNatural Twist Turn
Natural Twist TurnReverse Pivot
Reverse PivotQuick Open Reverse
Quick Natural Weave from PP
Quick Natural Weave from PPCurved Feather to Back Feather
Curved Feather to Back FeatherCurved Feather
Curved FeatherBack Feather
Back FeatherCurved Feather from PP
Curved Feather from PPNatural Zig-zag from PP
Natural Zig-Zag from PPFallaway Reverse & Slip Pivot
Fallaway Reverse & Slip PivotNatural Hover Telemark
Natural Hover TelemarkBounce Fallaway with Weave ending
Bounce Fallaway with Weave endingExtended Reverse Wave
Extended Reverse WaveCurved Three Step
Curved Three Step