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Intangible Assets and Goodwill (Details) - USD ($) $ in Millions	3 Months Ended				9 Months Ended		12 Months Ended
	Sep. 30, 2017	Jun. 30, 2017	Mar. 31, 2017	Sep. 30, 2016	Sep. 30, 2017	Sep. 30, 2016	Dec. 31, 2016
Intangible assets
Amortization of acquired intangible assets	$ 108.9			$ 99.7	$ 674.9	$ 281.4
Total intangible assets, gross	8,295.8				8,295.8		$ 7,742.3
Accumulated Amortization	(4,276.4)				(4,276.4)		(3,934.0)
Intangible assets, net	4,019.4				4,019.4		3,808.3
Payment made to Forward Pharma			$ 1,250.0
TECFIDERA intellectual property charges							454.8
Intangible Assets and Goodwill (Textual) [Abstract]
Accumulated impairment losses related to goodwill	0.0				0.0
Expected future amortization expense, 2017 (remaining three months)	106.8				106.8
Expected future amortization expense, 2018	421.3				421.3
Expected future amortization expense, 2019	404.0				404.0
Expected future amortization expense, 2020	389.6				389.6
Expected future amortization expense, 2021	256.6				256.6
Expected future amortization expense, 2022	244.7				244.7
TECFIDERA
Intangible assets
Amortization of acquired intangible assets	30.4				413.4
Increase in acquired and in-licensed rights and patents			$ 795.2
Out-licensed patents
Intangible assets
Cost	543.3				543.3		543.3
Accumulated Amortization	(532.7)				(532.7)		(523.6)
Net	10.6				$ 10.6		19.7
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	(2,675.8)				(2,675.8)		(2,634.3)
Net	329.5				$ 329.5		371.0
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	322.5				$ 322.5
Acquired and in-licensed rights and patents
Intangible assets
Cost	4,002.6				4,002.6		3,481.7
Accumulated Amortization	(1,067.9)				(1,067.9)		(776.1)
Net	2,934.7				$ 2,934.7		2,705.6
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 | SPINRAZA
Intangible assets
Increase in acquired and in-licensed rights and patents	40.0	$ 50.0			$ 150.0
Acquired and in-licensed rights and patents | Samsung Biosimilar Agreement [Member]
Intangible assets
Increase in acquired and in-licensed rights and patents	25.0
In Process Research and Development [Member]
Intangible assets
Indefinite lived intangible assets useful life					Indefinite until commercialization
Cost and Net	680.6				$ 680.6		648.0
Accumulated Amortization	0.0				$ 0.0		0.0
Trademarks and Trade Names [Member]
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
TYSABRI product | Acquired and in-licensed rights and patents
Intangible assets
Net	$ 2,293.9				$ 2,293.9

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