1. Introduction

This tutorial aims to guide you through the process of implementing smooth page transitions in a Vue.js application. By the end of this tutorial, you will have learned how to use Vue's native transition system to animate transitions between different routes in a Vue Router application.

What you will learn:
- The basics of Vue's transition system
- How to use Vue Router to manage routes
- How to animate transitions between different routes

Prerequisites:
- Basic understanding of Vue.js
- Familiarity with ES6 JavaScript syntax
- Basic understanding of CSS animations

2. Step-by-Step Guide

Vue provides a <transition> wrapper component, allowing you to add entering/leaving transitions for any element or component in the following context:
- Conditional rendering (using v-if)
- Conditional display (using v-show)
- Dynamic components
- Component root nodes

We will mainly focus on dynamic components and component root nodes since we are dealing with Vue Router.

3. Code Examples

Let's start with a basic Vue Router setup.

// main.js
import Vue from 'vue'
import VueRouter from 'vue-router'
import App from './App.vue'
import HomeComponent from './HomeComponent.vue'
import AboutComponent from './AboutComponent.vue'

Vue.use(VueRouter)

const routes = [
  { path: '/', component: HomeComponent },
  { path: '/about', component: AboutComponent }
]

const router = new VueRouter({
  routes // short for `routes: routes`
})

new Vue({
  router,
  render: h => h(App)
}).$mount('#app')

In your App.vue file, wrap the <router-view> component with <transition>.

<template>
  <div id="app">
    <transition name="slide">
      <router-view></router-view>
    </transition>
  </div>
</template>

The name="slide" attribute is important as it is used to generate the CSS classes that drive the animation. Vue automatically adds classes at different stages of the transition.

Here's an example of what your CSS could look like:

.slide-enter-active,
.slide-leave-active {
  transition: all 0.3s ease;
}

.slide-enter,
.slide-leave-to {
  transform: translateX(100%);
}

.slide-leave,
.slide-enter-to {
  transform: translateX(0);
}

4. Summary

In this tutorial, you learned how to use Vue's transition system and Vue Router to animate transitions between different routes. You learned how to use the <transition> wrapper component and how Vue automatically adds classes at different stages of the transition.

For further learning, you might want to explore Vue's other transition options, such as JavaScript Hooks and Transition Modes.

Additional resources:
- Vue.js Guide on Transitions & Animations
- Vue Router Guide

5. Practice Exercises

1. Create a Vue application with three routes (Home, About, Contact) and implement slide transitions between the pages.

2. Modify the previous exercise to implement a different transition effect (like fade or zoom).

3. Implement a complex animation using Vue's JavaScript Hooks.

Solutions and explanations will depend on the specific animations and configurations you choose. Remember, practice is the key to mastering any new concept, so keep experimenting with different transition effects and options.