Does Monopoly involve skill to a considerable degree?
You didn't lay out criteria in your question so I'm going to assume that what you're asking is: Let's say Bob diligently acquires as much skill as possible in Monopoly and practices with 50 or more games. If Bob plays several beginners (10 or fewer games - little study of the game), and no players know other players' skill level - is Bob highly likely to win?

The answer is yes. Monopoly definitely involves skill, and therefore Bob is highly likely to win that first game.

The most sophisticated and difficult skill involves working favorable trades. Though trading occurs only a few times a game, it is the primary means by which skill can cause the odds of winning to shift dramatically.

To make favorable trades, you must:


understand relative worth of different properties (you must know landing frequencies, development costs, etc.)
understand risk/reward
be able to quickly understand what your opponents care about, which in many cases will NOT be optimizing for greatest relative worth trades
be persuasive


There are also some simpler skills such as learning when it makes sense to buy a property and when to let it go up for auction, when it makes sense to start building houses (and how much money to keep in reserve), that the third house is the most valuable, etc.

Like Settlers of Catan, however, once it is clear who is the most skilled player, it is very easy for everyone to stop the most skilled player via trade embargos. I have had the experience several times of trouncing new opponents at Monopoly for a game or two and then losing more than average thereafter when my opponents refuse to trade with me. Actually - it's usually a little more gradual than that as first they just refuse to trade on my terms and start demanding more. And then they won't ever let me have a monopoly result from a trade. So then I resort to ever higher risk trades until I reach a point where nobody is willing to give me any trade I would want.

It is only when playing with fresh opponents that I have an opportunity to exert maximum skill, without fear that trading reputation will mean embargoes. That is why I carefully rephrased your question to assume lack of knowledge of the opponents. Because once it is clear who the most skilled player is in the game, it is very easy for opponents to gang up and actually cause the most skilled player to lose more often than average.

Side Note: several other answers imply that the luck of what you get has to be pretty good to even have a chance at making favorable trades. To that I say, you can make your own luck. For example, if you've studied Monopoly, you know that the two best monopolies to get in terms of risk/reward and Return on Investment are the oranges and light blues. So you may try trading for them earlier in the game. Many players are under the mistaken belief that Boardwalk is the best property. So if I obtain Boardwalk and I own one light blue, while the 2nd is owned by a different player and third by bank - I may offer Boardwalk for the light blue that is owned - and they think they are getting a steal. I now have two light blues and have created the possibility that I may get a monopoly if I get the third. So even though I had bad luck in not having 2 out of 3 of either light blue or orange, I have created a 2 out of 3 situation with one of the best two colors to increase my chances of getting lucky, or at least being able to trade for the 3rd.