How to reach max population in Cities: Skylines with no mods

1) ROADS - Start your city from the very beginning with all 4 lane roads and upgrade them to six lane decorated ASAP. This will greatly decrease the traffic in your city and help to reduce noise pollution and increase happiness. The increased maintenance cost is negligible.
2) ZONES and DISTRICTS - In the early game just follow the demand indicators as to what types of buildings you should zone for. Making small districts of specialized industry can be helpful as well to increase profitability of industry. That being said be aware that making large districts of oil and ore may not be feasible in the late game. Large swaths of farmland and medium-sized areas of timber industry will most likely persist to the end, but ore and oil producing industries will become largely abandoned if built in great abundance. I've found that oil and ore industries thrive best in small sections consisting of a few factories. As for residential and commercial, immediately switch to building high-density buildings as soon as they become available. It may be helpful to go back and rezone some of your previous low-density areas as well. After the Eden Project has been built (more about that below) the demand indicator will pretty much always show a low demand for residential, but they can still be built heavily and grow just fine. I recommend building your zones with a ratio of 4:3:2:1 of residential:commercial:office:industrial in the late game as an extremely rough estimate and should lead you to a balanced city with very few abandoned buildings.
3) BUSES - Build buses as soon as they unlock. Buses are cheap, greatly increase happiness, allow citizens access to different parts of the map, do not create pollution, decrease traffic, and will turn a profit. Make sure your different bus lines have stops next to each other to connect your bus lines with each other. This way citizens can hop bus lines to reach other areas of the city.
4) EDUCATION - Keep your education level as high as possible. This will help you build the Eden Project later because it provides the highly educated citizens which are required to work in office buildings and Level 3 industrial buildings. That being said once you unlock high density residential you should build 95% of your residential buildings as high density from then on. This is because the high density buildings house young adults which will attend your university and in turn become highly educated. Your first University will greatly increase the happiness and land value of nearby citizens so put it in a central location with many high-density residential nearby.
5) FREIGHT and CARGO - Connect regional freight and ocean cargo to your city via a local freight line. Do this by first connecting a cargo terminal to the regional rail line. Next build another cargo terminal right next to the regional terminal and connect them not with rail but with a loop of ROAD. This ensures that the international freight and the local freight trains do not mix. The freight will be brought over to the local line via trucks. I like this video if you're a visual learner.    • Cities Skylines Tutorial #4 - Public ...   Next, connect your major industrial centers with your local freight. You can do the same thing with your harbor by building a cargo terminal right outside of the harbor connected by a loop of road. This should be connected to the local freight line as well. Also, DO NOT join your local train passenger line with your local freight line. The lines will become too congested with trains.
6) EDEN PROJECT - You need to unlock the Eden Project to advance to max population. In order to build the Eden Project you will need to unlock the Official Park and the Business Park which require 10,000 office spaces and 20,000 commercial spaces respectively; therefore, having highly educated citizens to occupy office space and help upgrade your industrial buildings (which will supply goods to help upgrade your commercial buildings) is crucial. As you get closer to being able to build the Eden Project your city will be on the verge of not growing anymore. This will happen around 110-120k pop or so. You will likely have industrial areas that are becoming a nuisance with a lot of abandoned buildings at this time. Go through these areas and convert these abandoned industrial areas to office space. These office spaces should flourish and help unlock the Official Park. After the Eden Project is built and the game gets higher pop the amount of industrial spaces required becomes a little less, with only pockets of industry here and there suitable for expansion. Late in the game if your commercial areas are demanding goods building a small area of industry nearby should suffice.