Most of the main species of British tree are represented in the park, though it's a bit lacking in the hedgerow trees. There are privet hedges around the tennis & croquet lawns, a beech hedge around the cottages at the east end and some new holly bushes on Leamington Walk, but apart from some cute little parterres on the north side of Bruntsfield Links, there's not much else in the way of hedgerows.

There also hadn't been many conifers till recently, but from 2015 onwards, several attractive individuals have been planted, in particular the new pines and cedars.

Look out for these:

Alders and a map of where to spot some
Cherries & other fruit
Chestnuts (see map of horse chestnuts)
Conifers and map 
Elms and map 
Hawthorns & other Thorns, and map 
Maples, including Sycamores
Rowans and Whitebeams, and map
Willows and map

There are some exotic trees to spot, in particular:

Cedar of Lebanon
Foxglove Tree (see map)
Giant Redwood
Gingko Biloba
Golden Honey Locust Tree
Indian Bean Tree
Katsura Tree
Tulip Tree

A small row of new Magnolias has appeared on Bruntsfield Links in the small enclosed playpark and in May 2016 they unfurled their first flowers