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Types of Anchors
Danforth
This has become the most popular anchor as it is light weight and inexpensive with high holding power.It also sets very easily in sand, mud and soft clay.It doesn't set well in hard bottoms or grassy/weedy bottoms.Also it is prone to breaking loose if the angle of pull changes too much then only aan average ability to reset itself.They are still hard to beat overall if you are a recreational boater.I recomend a 1/2 boats length of chain minimum for any anchor system.They also make aluminum models of this anchor these are the highest holding power to weight anchors available.I favour these as a secondary anchor .They are lightweight which is nice if you have to take the dingy to go out and drop your anchor.Also they don't rust and they break down for easy storage .Downsides are they are expensive and because being light they are difficult to set in fast currents as they tend to plane a little.Also because of being lightweight iff they break loose they have difficulty resetting themselves.
CQR and Delta style anchors
Delta
CQR

These anchors are favoured a lot by more serious cruisers.Although they are rated at much heavier for a given boat size usually about 1 lb per foot of boat length and can take a little effort to set well.Once in they rarely break free and they have the ability to reset through changing angles of pull.They also do well in the more difficult hard clay as they are less likely to clog up.
Bruce and claw styles of Anchor

These are also a popular anchor amoungst more serious cruisers.They are lighter for a specific boat length than CQR/Plow anchors but still heavier than Danforths.They have reasonable ability to self reset through changing angles without coming out.They can be a little prone to clogging in certain types of clay and firm mud bottoms.
Rocking chair river anchors

These style anchors are primarily used on rivers by fisherman needing to anchor in fast current and reasonably deep water.These anchors are regularly used with scopes of 3:1 or less and still hold well.It is advisable to get a good anchor retrieval system as you may have to do it a lot in a days fishing.A good system is a EZ MARINE anchor puller.It's a good system as it not only makes anchor retrieval easy at allows you to untie to fight a fish then come back and pick up your spot again.I also recomend a 1/2 boat lengths worth of chain for these anchors.
Grappnel Anchors
This is a very lightweight anchor mainly used for dingies or canoes.They can also be used to retrieve items from the bottom by trying to snag them.