Intangible Assets and Goodwill (Details) - USD ($) $ in Millions	3 Months Ended			6 Months Ended
	Jun. 30, 2018	Jun. 30, 2017	Mar. 31, 2017	Jun. 30, 2018	Jun. 30, 2017	Dec. 31, 2017
Intangible assets
Total intangible assets, gross	$ 8,257.3			$ 8,257.3		$ 8,264.6
Amortization of acquired intangible assets	107.4	$ 117.5		211.3	$ 566.0
Accumulated Amortization	(4,596.0)			(4,596.0)		(4,385.0)
Intangible assets, net	3,661.3			3,661.3		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			0.0
Expected future amortization expense, 2018 (remaining six months)	215.8			215.8
Expected future amortization expense, 2019	402.6			402.6
Expected future amortization expense, 2020	380.9			380.9
Expected future amortization expense, 2021	255.0			255.0
Expected future amortization expense, 2022	242.3			242.3
Expected future amortization expense, 2023	211.2			211.2
Out-licensed patents
Intangible assets
Cost	543.3			543.3		543.3
Accumulated Amortization	(539.9)			(539.9)		(535.6)
Net	3.4			$ 3.4		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		3,005.3
Accumulated Amortization	(2,713.1)			(2,713.1)		(2,689.0)
Net	292.2			$ 292.2		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	285.8			$ 285.8
Acquired and in-licensed rights and patents
Intangible assets
Cost	3,974.2			3,974.2		3,971.4
Accumulated Amortization	(1,343.0)			(1,343.0)		(1,160.4)
Net	2,631.2			$ 2,631.2		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 | TYSABRI
Intangible assets
Net	2,120.8			$ 2,120.8
Acquired and in-licensed rights and patents | TECFIDERA
Intangible assets
Net	291.4			$ 291.4
In Process Research and Development
Intangible assets
Indefinite lived intangible assets useful life				Indefinite until commercialization
Cost and Net	670.5			$ 670.5		680.6
Accumulated Amortization	0.0			$ 0.0		0.0
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