Intangible Assets and Goodwill (Details) - USD ($) $ in Millions	3 Months Ended			9 Months Ended
	Sep. 30, 2018	Sep. 30, 2017	Mar. 31, 2017	Sep. 30, 2018	Sep. 30, 2017	Dec. 31, 2017
Intangible assets
Total intangible assets, gross	$ 8,067.7			$ 8,067.7		$ 8,264.6
Accumulated Amortization	(4,688.7)			(4,688.7)		(4,385.0)
Intangible assets, net	3,379.0			3,379.0		3,879.6
Contingent consideration	87.9	$ (30.0)		91.6	$ (61.2)
Amortization of acquired intangible assets	281.9	$ 108.9		493.2	$ 674.9
Payment made to Forward Pharma			$ 1,250.0
Intangible Assets and Goodwill (Textual) [Abstract]
Accumulated impairment losses related to goodwill	0.0			0.0
Expected future amortization expense, 2018 (remaining three months)	91.7			91.7
Expected future amortization expense, 2019	367.0			367.0
Expected future amortization expense, 2020	366.8			366.8
Expected future amortization expense, 2021	249.4			249.4
Expected future amortization expense, 2022	250.5			250.5
Expected future amortization expense, 2023	230.0			230.0
Out-licensed patents
Intangible assets
Cost	543.3			543.3		543.3
Net	1.7			1.7		7.7
Accumulated Amortization	(541.6)			$ (541.6)		(535.6)
Out-licensed patents | Minimum
Intangible assets
Estimated life, (in years)				13 years
Out-licensed patents | Maximum
Intangible assets
Estimated life, (in years)				23 years
Developed technology
Intangible assets
Cost	3,005.3			$ 3,005.3		3,005.3
Net	281.3			281.3		316.3
Accumulated Amortization	(2,724.0)			$ (2,724.0)		(2,689.0)
Developed technology | Minimum
Intangible assets
Estimated life, (in years)				15 years
Developed technology | Maximum
Intangible assets
Estimated life, (in years)				23 years
Developed technology | AVONEX
Intangible assets
Net	275.3			$ 275.3
Acquired and in-licensed rights and patents
Intangible assets
Cost	3,974.2			3,974.2		3,971.4
Net	2,551.1			2,551.1		2,811.0
Accumulated Amortization	(1,423.1)			$ (1,423.1)		(1,160.4)
Acquired and in-licensed rights and patents | Minimum
Intangible assets
Estimated life, (in years)				4 years
Acquired and in-licensed rights and patents | Maximum
Intangible assets
Estimated life, (in years)				18 years
Acquired and in-licensed rights and patents | TYSABRI
Intangible assets
Net	2,073.6			$ 2,073.6
Acquired and in-licensed rights and patents | TECFIDERA
Intangible assets
Net	262.6		795.2	$ 262.6
Amortization of acquired intangible assets			$ 328.2
In Process Research and Development
Intangible assets
Indefinite lived intangible assets useful life				Indefinite until commercialization
Cost and Net	480.9			$ 480.9		680.6
Accumulated Amortization	0.0			$ 0.0		0.0
Amortization of acquired intangible assets	189.3
Trademarks and Trade Names
Intangible assets
Indefinite lived intangible assets useful life				Indefinite
Cost and Net	64.0			$ 64.0		64.0
Accumulated Amortization	0.0			0.0		$ 0.0
PLSR | In Process Research and Development
Intangible assets
Amortization of acquired intangible assets	60.0
TGN
Intangible assets
Contingent consideration	89.6
TGN | In Process Research and Development
Intangible assets
Cost and Net	41.8			$ 41.8
Amortization of acquired intangible assets	$ 129.3