Intangible Assets and Goodwill (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2018	Mar. 31, 2017	Dec. 31, 2017
Intangible assets
Total intangible assets, gross	$ 8,283.7		$ 8,264.6
Amortization of acquired intangible assets	103.9	$ 448.5
Accumulated Amortization	(4,489.2)		(4,385.0)
Intangible assets, net	3,794.5		3,879.6
Payment made to Forward Pharma		$ 1,250.0
Intangible Assets and Goodwill (Textual) [Abstract]
Accumulated impairment losses related to goodwill	0.0
Expected future amortization expense, 2018 (remaining nine months)	330.7
Expected future amortization expense, 2019	402.6
Expected future amortization expense, 2020	379.5
Expected future amortization expense, 2021	255.0
Expected future amortization expense, 2022	242.2
Expected future amortization expense, 2023	211.2
Out-licensed patents
Intangible assets
Cost	543.3		543.3
Accumulated Amortization	(537.8)		(535.6)
Net	$ 5.5		7.7
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
Accumulated Amortization	(2,700.5)		(2,689.0)
Net	$ 304.8		316.3
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	$ 298.2
Acquired and in-licensed rights and patents
Intangible assets
Cost	3,974.7		3,971.4
Accumulated Amortization	(1,250.9)		(1,160.4)
Net	$ 2,723.8		2,811.0
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 | TECFIDERA
Intangible assets
Net	$ 322.5
In Process Research and Development
Intangible assets
Indefinite lived intangible assets useful life	Indefinite until commercialization
Cost and Net	$ 696.4		680.6
Accumulated Amortization	$ 0.0		0.0
Trademarks and Trade Names
Intangible assets
Indefinite lived intangible assets useful life	Indefinite
Cost and Net	$ 64.0		64.0
Accumulated Amortization	0.0		$ 0.0
TYSABRI | Acquired and in-licensed rights and patents
Intangible assets
Net	$ 2,178.4