When you hear the word "anarchy", is this the picture that comes to your mind? If so, to quote Inigo Montoya: "I do not think it means what you think it means". The popular image of anarchy is of people rioting in the streets, burning cars and smashing storefronts. The news media promotes this image because it would like you to believe that this behavior is the inevitable result of anarchy and you must therefore embrace government who will protect you. But the truth is, this is the exact opposite of anarchy.
According to wikipedia, the etymology of the word anarchy is the ancient Greek word "ἀναρχία (anarchia), which combines ἀ (a), 'not, without' and ἀρχή (arkhi), 'ruler, leader, authority.' Thus, the term refers to a person or society 'without rulers' or 'without leaders'". Anarchy is a philosophy where all initiation of force is immoral, including government. Instead, all interactions between people are completely voluntary. There is no government police force to enforce an arbitrary, or voted upon set of laws that govern your behavior. In anarchy, people voluntarily agree to how they will interact with one another. This includes prohibited behavior, such as theft or assault, and the enforcement mechanism (e.g. a private police force).
There is much more to anarchy than this brief, simplistic explanation, and I'm guessing some anarchists will have philosophical quibbles with my description. And although I agree with much of the philosophy, I have reservations about the achievability of an anarchistic society. But more important is the recognition that anarchy is one of the most peaceful and moral philosophies, and the act of destroying property is completely antithetical to their belief in voluntary interaction. Anarchists would never engage in the destructive activities the media attributes to them. Personally, I know quite a few anarchists, and I trust them far more than I do traditional conservatives and progressives, who won't hesitate to attempt to control my life through their "laws" and police forces.
So, if the idea of peace and harmony, and improvement in conditions across the world is important to you, find an anarchist and give her a hug. Then talk with her about her philosophy and learn more about it. There are plenty of resources on the internet for you to learn about Anarchy, but I won't link to them here. Instead, I highly recommend you start with a simple conversation with an anarchist friend, or post a comment below.
Photo Credits
Picture of riot taken from: http://globaleconomicanalysis.blogspot.com/2014/11/riots-in-brussels-100000-protest.html