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Income Taxes (Narrative) (Details) (USD $)
 12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Dec. 31, 2011
Income Tax Contingency [Line Items]        
Excess Tax Benefit from Share-based Compensation, Operating Activities $ 500,000us-gaap_ExcessTaxBenefitFromShareBasedCompensationOperatingActivities      
Income tax expense, restructuring domestic TRS 2,600,000amt_IncomeTaxExpenseRestructuringDomesticTRS 21,500,000amt_IncomeTaxExpenseRestructuringDomesticTRS    
Valuation allowance 141,200,000us-gaap_DeferredTaxAssetsValuationAllowance 136,000,000us-gaap_DeferredTaxAssetsValuationAllowance    
Undistributed Earnings of Foreign Subsidiaries 391,000,000us-gaap_UndistributedEarningsOfForeignSubsidiaries      
Excess tax benefit from the exercise of employee stock options 300,000,000us-gaap_IncomeTaxEffectsAllocatedDirectlyToEquityEmployeeStockOptions      
Tax credit carryforward 2,100,000us-gaap_TaxCreditCarryforwardAmount      
Unrecognized tax benefits that would impact the ETR 31,900,000us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate 31,100,000us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate    
Impact of uncertain tax positions, minimum 0us-gaap_SignificantChangeInUnrecognizedTaxBenefitsIsReasonablyPossibleEstimatedRangeOfChangeLowerBound      
Impact of uncertain tax positions, maximum 18,200,000us-gaap_SignificantChangeInUnrecognizedTaxBenefitsIsReasonablyPossibleEstimatedRangeOfChangeUpperBound      
Unrecognized Tax Benefits, Decrease Resulting from Settlements with Taxing Authorities     2,100,000us-gaap_UnrecognizedTaxBenefitsDecreasesResultingFromSettlementsWithTaxingAuthorities  
Decrease in unrecognized tax benefits, lapse of applicable statute of limitations 5,349,000us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations [1] 1,218,000us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations [1] 4,926,000us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations [1]  
Unrecognized tax benefits, income tax penalties and interest (3,400,000)us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense 3,400,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense (2,900,000)us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense  
Unrecognized tax benefits 31,947,000us-gaap_UnrecognizedTaxBenefits 32,545,000us-gaap_UnrecognizedTaxBenefits 34,337,000us-gaap_UnrecognizedTaxBenefits 38,886,000us-gaap_UnrecognizedTaxBenefits
Unrecognized tax benefits, income tax penalties and interest accrued 24,900,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued 30,900,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued    
Other Noncurrent Liabilities        
Income Tax Contingency [Line Items]        
Unrecognized tax benefits 31,900,000us-gaap_UnrecognizedTaxBenefits
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherNoncurrentLiabilitiesMember		 32,500,000us-gaap_UnrecognizedTaxBenefits
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherNoncurrentLiabilitiesMember		    
Federal        
Income Tax Contingency [Line Items]        
Operating Loss Carryforwards 939,775,000us-gaap_OperatingLossCarryforwards
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_DomesticCountryMember		      
Subsidiaries | Federal        
Income Tax Contingency [Line Items]        
Operating Loss Carryforwards $ 647,300,000us-gaap_OperatingLossCarryforwards
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_DomesticCountryMember
/ us-gaap_RelatedPartyTransactionsByRelatedPartyAxis
= us-gaap_SubsidiariesMember		      
[1] (1) Includes $2.1 million of effective settlements for the year ended December 31, 2012.