Wikipedia has a very useful entry on this subject, which might lead one to wonder what, in fact, is a 'Libertarian'. Consequentially, it might even be argued that 'Libertarians' are 'Anarchists', to a certain degree.
True liberty involves an equality of authority – we each rule our own lives, but do not get to rule over others. Each individual exists for his or her own sake. Nobody has a better claim to the life of any person than the person who actually lives it. Government inherently takes a position of superiority over the people. The state is the concentrated force of authority which invades liberty to extract wealth and compel obedience to whatever has been legislated by the most powerful elements of society - the political elite. On could summarise 'Government' as existing solely to protect and serve those policos in power at the expense of the ruled. Where 'government' has gone wrong for decades is that it invariably wields a club - to subjugate - in achieving it's aims, and in so doing grabs more and more of what could be termed 'freedoms' from the individual in the process.
For an anarchist, the state is the enemy - consequently those of us who hanker for 'minimum' government - and through that 'local government' - are, to a certain extent, now anarchists in that we also consider the state 'the enemy'. As with 'anarchists', 'libertarians' now believe that our present form of government is the number one thing that must be dismantled. Identify anyone who admits to being an anarchist and he/she will be identified as someone opposed to the system because of he/she doesn’t like authority - Libertarians?
Where libertarians will argue that they are different from anarchists is that libertarians believe in a form of government, albeit 'small' or 'minimum' government, one that limits itself to 'national' matters - foreign policy, defence - and designates basic standards that are required in respect of education, health care, a judicial system for example and leaves how those 'basic standards' are implemented - and improved upon, if so wished - within a local authority area to those that live there.
Just a few thoughts for a dull Saturday evening.........................