Can someone offer a type of tree that has a deep root system, but not wide - as it will be planted near a patio and building. And also one that offers nice privacy and shade, but which does not produce too much litter?
Fig trees tolerate restricted root space (in fact that’s how they are typically induced to fruit - by growing them in a pit lined with paving slabs.
However, they probably don’t meet your requirements with respect to tidiness - the leaves are large and easy to clear up, but the fruits make a mess if they fall and rot.
Do you want to grow this tree in Siberia or Singapore? Location is kind of important.
Mangetout, there are around a thousands species of fig tree. The vast majority of them are utterly unsuitable for planting anywhere near habitation. The roots are notorious for destroying concrete foundations and penetrating water and sewage lines. They are also the absolute last plants you would recommend to someone who wants a root system that is not wide. An average mature fig tree would have a root system that covers about a hectare. A large specimen will happily cover a hundred hectares.
I’m guessing Chicago.
Obviously I was talking about the common fig (Ficus carica) - I stand corrected on the extent and power of the root system.
Perhaps a better solution to your requirements might be construction of a pergola, and clothe it with a suitable climbing plant.
If you’re in a warm climate, a palm. If not, a pine.
Just assume that the breadth of the crown defines the spread of the roots. If you can get a myrtle to a good size, they are evergreen, and you can use their leaves to season your soup.
You may want to search for the term “tap root” - this is a single, massive root which (tries) to go straight down.
You don’t want pines.
The classic shade tree is/was the Elm - don’t know if they were all wiped out by Dutch Elm Disease or if another species has replaced them.
I would suggest looking into the Linden. While it does develop surface roots, (at least in the abominable clay in which ours sits), it does not have any reputation for invasive roots that would tear up sidewalks or patios. It gives good shade and is not known as a “messy” tree. (If attacked by aphids, it can drop sap, but aphid infestations are generally easy to control. I have not even suffered such an infestation in Northeast Ohio.)
Worth thinking outside your original parameters, OP
An acquaintance of mine with a similar problem bought a dead tree trunk with a few cut off branches and set it in a concrete base. He has Clematis growing up it and it is quite a talking point. Of course it looks pretty bare in the winter but then so do deciduous trees.
In the UK, planting trees near the house can cause big problems with insurance due to the damage they can cause. Elms have deep roots but suck all the available water from the ground and actively search for land drains etc.
A local cricket pitch had six fully grown elms at one end and it had never become waterlogged in living memory. Since they were felled due to disease, the ground has really suffered from water.
It’s a funny sketch, but quite untrue. Linden (Tilia spp.) Flowers have a very nice fragrance.
Bradford pear is popular in my area. My dad planted three. Beautiful white flowers in Spring time. They don’t produce any fruit and stay reasonably compact. about 12 ft
heres one with flowers. thats a typical size too
heres one with just the leaves
http://www.hrwc.net/images/invasiveplants/callerypear.jpg
Assuming that the OP is in Chicago, he/she might want to review this PDF document from the city government listing trees appropriate in urban areas.
Funny. This tree is one that I’ve described in similar terms to Waltzes with Cacti’s observation. 
Honestly, they smell like … well, dirty laundry is a kinder term I suppose.
Note that your foliage picture seems to be from a list of invasive species. Bradford pears have multicolored fall foliage, pure-white spring flowers, and an even, symmetrical lollipop shape … but they’re also relatively short-lived and have weak branches, making them extremely susceptible to dropping limbs or causing other damage during a storm.
Linden trees attract stinging insects, which is not something you want near a patio. Some guy got a bright idea to plant a bunch in the courtyard at work and it’s essentially unusable when the trees are producing that sticky sap that they do.
Not lindens. The Bradford pear has a blossom smell which has provoked that comparison, as has the rowan or mountain ash blossom smell.
Don’t recall encountering a Bradford pear, but to me rowan blooms smell like rancid grease. No joke; the first time I noticed one, I actually went and checked the sewer lift station to see if it was overflowing. 
The young leaves can be eaten in salads and sandwiches, but in my experience, there’s about a 7 day window after emergence of leaves, before they are hopelessly infested with aphids, shitting sugar water everywhere, both on and off the tree (some people prefer the leaves for eating after they become coated with sweet, sticky aphid shit, but - despite my username - I don’t fancy it).
Lime (linden) trees are lovely, but I would not plant one over a patio.
I imagine there must have been threads on this question, but I’m really perplexed by this statement. My own doesn’t have any smell, and neither does any one else’s that I’ve been near (don’t ask). Mrs. CC also report that in her pre-me experience, she never detected any odor from any other guy. Does some semen actuallly have a noticeable smell?